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Page No 14:

Question 1:

Which of the following conclusions could not be derived from Rutherford’s α-particle scattering experiment?
(i) Most of the space in the atom is empty.
(ii) The radius of the atom is about 10–10 m while that of nucleus is 10–15 m.
(iii) Electrons move in a circular path of fixed energy called orbits.
(iv) Electrons and the nucleus are held together by electrostatic forces of attraction.

Answer:

Rutherford’s α-particle scattering experiment gave the following conclusions:
1- Most of the space in the atom is empty as most of the alpha particle passed undeflected through the atom.
2- The radius of the atom is about 10–10 m while that of nucleus is 10–15 m , this signifies that size of atom is 105 times more than size of nucleus.
3- Electrons and the nucleus are held together by electrostatic forces of attraction.

But, the conclusion that electrons move in a circular path of fixed energy called orbits was given by Bohr and not Rutherford.

Hence, the correct answer is option C.


 

Page No 14:

Question 2:

Which of the following options does not represent ground state electronic configuration of an atom?
(i) 1s2 2s2 2p6 3s2 3p6 3d8 4s2
(ii) 1s2 2s2 2p6 3s2 3p6 3d9 4s2
(iii) 1s2 2s2 2p6 3s2 3p6 3d10 4s1
(iv) 1s2 2s2 2p6 3s2 3p6 3d5 4s1

Answer:

The ground state electronic configuration along with their corresponding elements are mentioned below:
1s2 2s2 2p6 3s2 3p6 3d8 4s2 - Ground state electronic configuration of Ni.
1s2 2s2 2p6 3s3p6 3d10 4s1- Ground state electronic configuration of Cu.
1s2 2s2 2p6 3s2 3p6 3d5 4s1- Ground state electronic configuration of Cr.

Therefore, 1s2 2s2 2p6 3s2 3p6 3d9 4s2 is not the ground state electronic configuration of Cu due to symmetrical electronic configuration and electron exchange energy Cu exist in 1s2 2s2 2p6 3s3p6 3d10 4sground state electronic configuration.

Hence, the correct answer is option B.

Page No 14:

Question 3:

The probability density plots of 1s and 2s orbitals are given in Fig. 2.1:

The density of dots in a region represents the probability density of finding electrons in the region.
On the basis of above diagram which of the following statements is incorrect?
(i) 1s and 2s orbitals are spherical in shape.
(ii) The probability of finding the electron is maximum near the nucleus.
(iii) The probability of finding the electron at a given distance is equal in all directions.
(iv) The probability density of electrons for 2s orbital decreases uniformly as distance from the nucleus increases.

Answer:

s-orbitals are spherical in shape, the probability of finding electron is maximum near the nucleus and the probability of finding the electron at a given distance is equal in all directions as the number of angular nodes are zero (l=0).

For 1s orbital as number of radial nodes is zero hence maximum electron density is at nucleus and decreases sharply on moving away from nucleus.
In case of 2s-orbital, number of  angular nodes = 2-1 = 1. Thus, it has two maxima separated by a region of a nodal surface. The probability density is maximum near the nucleus and decreases sharply to zero and then start increasing again and after reaching a maxima falls abruptly. Hence, the probability density of electrons for 2s orbital decreases uniformly as distance from the nucleus increases is not a correct statement.

Hence, the correct answer is option D. 



Page No 15:

Question 4:

Which of the following statement is not correct about the characteristics of cathode rays?
(i) They start from the cathode and move towards the anode.
(ii) They travel in straight line in the absence of an external electrical or magnetic field.
(iii) Characteristics of cathode rays do not depend upon the material of electrodes in cathode ray tube.
(iv) Characteristics of cathode rays depend upon the nature of gas present in the cathode ray tube.

Answer:

Following are the characteristics of cathode rays :
1- Cathode rays are the rays which contain negatively charged particle hence they move from cathode (negative terminal) to anode (positive terminal)
2-In the absence of an external electric or magnetic field these rays travel in straight line while in presence of external electric and magnetic field these rays behave in the similar manner as negatively charged particle would behave.
3- Characteristics of cathode rays do not depend upon the material of electrodes in cathode ray tube and upon the nature of gas present in the cathode ray tube as cathode ray always consist of electrons, no matter what is the nature of electrode used or what is the nature of gas used.

As, characteristics of cathode rays do not depend upon the nature of gas present in the cathode ray tube.

Hence, the correct answer is option D.

Page No 15:

Question 5:

Which of the following statements about the electron is incorrect?
(i) It is a negatively charged particle.
(ii) The mass of electron is equal to the mass of neutron.
(iii) It is a basic constituent of all atoms.
(iv) It is a constituent of cathode rays.

Answer:

The following are the characteristics of an electron:
1-An electron is a negatively charged particle.
2-The mass of electron is 9.1×10-31 kg which is very small in comparison to the mass of neutron.
3-An electron is basic constituent of all the atoms.
4-It is a constituent of cathode rays.

Hence, the correct answer is option B.

Page No 15:

Question 6:

Which of the following properties of atom could be explained correctly by Thomson Model of atom?
(i) Overall neutrality of atom.
(ii) Spectra of hydrogen atom.
(iii) Position of electrons, protons and neutrons in atom.
(iv) Stability of atom.

Answer:

Thomson proposed a plum pudding model of atom. According to Thomson Model, an atom is a uniform sphere of positively charged particle and equal number of electrons are embedded on this positively charged sphere. Hence, overall neutrality of atom was explained by Thomson. 
While spectra of hydrogen atom, position of electrons, protons and neutrons in atom and stability of atom was explained by Bohr Model of atom.

Hence, the correct answer is option A.

Page No 15:

Question 7:

Two atoms are said to be isobars if.
(i) they have same atomic number but different mass number.
(ii) they have same number of electrons but different number of neutrons.
(iii) they have same number of neutrons but different number of electrons.
(iv) sum of the number of protons and neutrons is same but the number of protons is different.

Answer:

Two atoms are said to be isobars if they have same mass number but different atomic number or if sum of the number of protons and neutrons is same but the number of protons is different.

If they have same atomic number but different mass number they are called isotopes.

Hence, the correct answer is option D.

Page No 15:

Question 8:

The number of radial nodes for 3p orbital is __________.
(i) 3
(ii) 4
(iii) 2
(iv) 1

Answer:

Number of radial nodes is given by the formula (n-l-1)  where  n is principal quantum number and is azimuthal quantum number.

For 3p orbital n is 3 and  is 1. So, the number of radial nodes is 3-1-1 that is equal to 1.

Hence, the correct answer is option D.
 



Page No 16:

Question 9:

Number of angular nodes for 4d orbital is __________.
(i) 4
(ii) 3
(iii) 2
(iv) 1

Answer:

Number of angular nodes is given by the value of l (azimuthal quantum number). 

As the value of for 4d is 2 so, number of angular nodes for 4d orbital would be given as 2.

Hence, the correct answer is option C.

Page No 16:

Question 10:

Which of the following is responsible to rule out the existence of definite paths or trajectories of electrons?
(i) Pauli’s exclusion principle.
(ii) Heisenberg’s uncertainty principle.
(iii) Hund’s rule of maximum multiplicity.
(iv) Aufbau principle.

Answer:

Heisenberg’s uncertainty principle states that the position and velocity of an electron cannot both be measured simultaneously with 100% accuracy. Hence, it is responsible to rule out the existence of definite paths or trajectories of an electron, as it is not possible to know the exact path of an electron at a given time.

Hence the correct answer is option B.

Page No 16:

Question 11:

Total number of orbitals associated with third shell will be __________.
(i) 2
(ii) 4
(iii) 9
(iv) 3

Answer:

Total number of orbitals associated with a given shell is given by the formula n, where n is principal quantum number. Hence the total number of orbitals in 3rd shell would be 32 that is 9. These orbitals would be present in sub shell 3s, 3p and 3d. 3s contain 1 orbital, 3p contain 3 orbitals, 3d contains 5 orbitals. Therefore, in total 9 orbitals are present.

Hence the correct answer is option C.

Page No 16:

Question 12:

Orbital angular momentum depends on __________.
(i) l
(ii) n and l
(iii) n and m
(iv) m and s

Answer:

Orbital angular momentum is given by the formula l(l+1) h4π . Hence the value of orbital angular momentum depends on the value of l
Hence, the correct answer is option A.

Page No 16:

Question 13:

Chlorine exists in two isotopic forms, Cl-37 and Cl-35 but its atomic mass is 35.5. This indicates the ratio of Cl-37 and Cl-35 is approximately
(i) 1 : 2
(ii) 1 : 1
(iii) 1 : 3
(iv) 3 : 1

Answer:

Let, the percentage abundance of Cl-37 be A

Let, the percentage abundance of Cl-35 be B

Let, the molar mass of Cl-37 be M1 = 37

Let, the molar mass of Cl-35 be M2 = 35

A + B = 100

B = 100 - A

Mavg M1×A+M2×BA+B

35.5 = 37×A+35(100-A)100

35.5 = 37×A+3500-35×A100

Hence, A = 25 

B = 100 - 25 = 75 

AB= 2575=13

Thus, the ratio of Cl-37 and Cl-35 is approximately 1:3.

Hence, the correct answer is option C.

Page No 16:

Question 14:

The pair of ions having same electronic configuration is __________.
(i) Cr3+, Fe3+
(ii) Fe3+, Mn2+
(iii) Fe3+, Co3+
(iv) Sc3+, Cr3+

Answer:

The electronic configuration of Cr = [Ar] 3d5 4s1

                                                Cr3+ = [Ar] 3d3 4s0

the electronic configuration of Fe =  [Ar] 3d6 4s2

                                               Fe3+ = [Ar] 3d5 4s0

the electronic configuration of Mn = [Ar] 3d5 4s2

                                              Mn2+ = [Ar] 3d5 4s0

the electronic configuration of Co = [Ar] 3d7 4s2

                                              Co3+ = [Ar] 3d6 4s0

the electronic configuration of Sc = [Ar] 3d1 4s2

                                              Sc3+ = [Ar] 3d0 4s0 [noble gas configuration]

Thus, electronic configuration of Fe3+ is same as Mn2+ that is [Ar] 3d5 4s0.

Hence, the correct answer is option B. 
 

Page No 16:

Question 15:

For the electrons of oxygen atom, which of the following statements is correct?
(i)   Zeff for an electron in a 2s orbital is the same as Zeff for an electron in a 2p orbital.
(ii) An electron in the 2s orbital has the same energy as an electron in the 2p orbital.
(iii) Zeff for an electron in 1s orbital is the same as Zeff for an electron in a 2s orbital.
(iv) The two electrons present in the 2s orbital have same spin quantum numbers ms but of opposite sign.

Answer:

According pauli exclusion principle, no two electrons present in the same orbital can have same set of all the four quantum numbers. So, the correct statement is that, two electrons present in 2s orbital have same spin quantum numbers mbut of opposite sign according to pauli exclusion principle.

Hence, the correct answer is option D.



Page No 17:

Question 16:

If travelling at same speeds, which of the following matter waves have the shortest wavelength?
(i) Electron
(ii) Alpha particle (He2+)
(iii) Neutron
(iv) Proton

Answer:

We know, λ =hmv. For same value of v (velocity), larger the value of m (mass), shorter is the λ (wavelength).
Since, alpha particles have the largest mass, they have the shortest wavelength.

Hence, the correct answer is option B.

Page No 17:

Question 17:

In the given question two or more options may be correct.
Identify the pairs which are not of isotopes?
(i) X612, X613

(ii) X1735, Y1737

(iii) X614, Y714

(iv) X48, Y58

Answer:

Isotopes are species of same elements having different mass number (no. of protons + no. of neutrons) , but they have the same atomic number (number of protons). Therefore, the entities (iii) and (iv) are not isotopes as they have different atomic numbers.

Options (i) and (ii)  are definitely isotopes.

Hence, the correct answers are options C and D.

Page No 17:

Question 18:

In the given question two or more options may be correct.
Out of the following pairs of electrons, identify the pairs of electrons present in degenerate orbitals :
(i) 
an=3,l=2,ml=-2,ms=-12bn=3,l=2,ml=-1,ms=-12
(ii)
an=3,l=1,ml=1,ms=+12bn=3,l=2,ml=1,ms=+12

(iii)
an=4,l=1,ml=1,ms=+12bn=3,l=2,ml=1,ms=+12

(iv)
an=3,l=2,ml=+2,ms=-12bn=3,l=2,ml=+2,ms=+12

Answer:

Degenerate orbital means orbital having same energies. And the energy of an electron in a multi-electron system of atoms depends on the value of principal quantum number (n) and the azimuthal quantum number ( l) as well. If the value of n and l is same, that means the orbitals are degenerate.

(i) (a) n = 3, l = 2, ml = –2, ms = minus1 half and (b) n = 3, l = 2, m= –1, ms= −1 half
(iv) (a) n = 3, l = 2, ml = +2, ms = − 1 halfand (b) n = 3, l = 2, ml = +2, ms = +1 half 

have n and l values as equal so they are degenerate.

Hence the correct answers are options A and D.



Page No 18:

Question 19:

In the given question two or more options may be correct.
Which of the following sets of quantum numbers are correct?
 

  n l ml
(i)  1  1 + 2
(ii)  2  1 +1
(iii)  3  2  –2
(iv)  3  4  –2


 

Answer:

If n = 1, l ≠ 1. Hence, (i) is wrong.
If n = 2, l= 0, 1. For l = 1, m = -1, 0, +1. Hence (ii) is correct.
If n = 3, l= 0, 1, 2. For l = 2, m = -2, -1, 0, +1, +2. Hence (iii) is correct.
If n = 3, l ≠4. Hence, (iv) is wrong.

Hence, the correct answers are options B and C.

Page No 18:

Question 20:

In the given question two or more options may be correct.
In which of the following pairs, the ions are iso-electronic?
(i) Na+, Mg2+
(ii) Al3+, O
(iii) Na+, O2–
(iv) N3–, Cl

Answer:

Na+, Mg2+ have 10 electrons.

Na+, O2– have 10 electrons

As, we know iso-electronic species are the species that have the same number of electrons.

Hence, the correct answers are options A and C
 

Page No 18:

Question 21:

In the given question two or more options may be correct.
Which of the following statements concerning the quantum numbers are correct?
(i) Angular quantum number determines the three dimensional shape of the orbital.
(ii) The principal quantum number determines the orientation and energy of the orbital.
(iii) Magnetic quantum number determines the size of the orbital.
(iv) Spin quantum number of an electron determines the orientation of the spin of electron relative to the chosen axis.

Answer:

Azimuthal quantum number or l gives the value of orbital angular momentum of a certain orbital. And it defines the 3-D shape of an orbital by introducing the concept of angular momentum.
Spin quantum number ms gives the value of spin angular momentum of an electron as electron rotates around its axis, therefore besides having charge and mass an electron also has a certain orientation of the spin relative to the chosen axis which gives rise to the concept of spin angular quantum number (ms).
Hence statements (i) and (iv) are correct.

Hence, the correct answers are options A and D.

Page No 18:

Question 22:

Arrange s, p and d sub-shells of a shell in the increasing order of effective nuclear charge (Zeff) experienced by the electron present in them.

Answer:

Zeff experienced by s sub-shell is maximum while d sub-shell is minimum , this is because s subshell is spherically symmetrical therefore it has maximum penetration power and hence, it remains nearer to the nucleus and experience maximum Zeff. While d subshell have double dumbbell shape hence, it is more diffused and therefore have minimum penetration power, it stays away from the nucleus and experiences minimum  Zeff.
Hence, the value of Zeff  in increasing order is given as d<p<s.
 

Page No 18:

Question 23:

Show the distribution of electrons in oxygen atom (atomic number 8) using orbital diagram.

Answer:

Oxygen atomic number is 8.
Electronic configuration is 1s² 2s² 2p⁴.
Distribution of electrons in orbitals is as follows:

 

Page No 18:

Question 24:

Nickel atom can lose two electrons to form Ni2+ ion. The atomic number of nickel is 28. From which orbital will nickel lose two electrons.

Answer:

Atomic number of nickel is 28 and its electronic configuration is as follows:
1 s squared 2 s squared 2 p to the power of 6 3 s squared 3 p to the power of 6 4 s squared 3 d to the power of 8
In N i to the power of 2 plus end exponent, there will be two electrons less than the number of electrons present in a neutral nickel atom.
Therefore, the electronic configuration is as follows:
1 s squared 2 s squared 2 p to the power of 6 3 s squared 3 p to the power of 6 4 s to the power of 0 3 d to the power of 10
Hence, Nickel loses two electrons from 4s orbital as the 4th shell is the outermost shell of the atom
       

 

Page No 18:

Question 25:

Which of the following orbitals are degenerate?
3dxy, 4dxy 3dz2, 3dyz, 4dyz, 4dz2

Answer:

Degenerate orbitals are the one, which have same values of n and l, that is same values of principal and azimuthal quantum numbers.
Hence, 3dxy 3dz2 are degenerate orbitals and also 4dxy4dyz4dz2 are degenerate orbitals.
 



Page No 19:

Question 26:

Calculate the total number of angular nodes and radial nodes present in 3p orbital.

Answer:

For 3p orbital, n = 3, = 1
Number of angular nodes = =1
Number of radial nodes = n - l -1 = 3-1-1 = 1

Hence, number of angular node is 1 and number of radial nodes is also 1.

Page No 19:

Question 27:

The arrangement of orbitals on the basis of energy is based upon their (n + l ) value. Lower the value of (n + l ), lower is the energy. For orbitals having same values of (n + l ), the orbital with lower value of n will have lower energy.

I. Based upon the above information, arrange the following orbitals in the increasing order of energy.

(a) 1s, 2s, 3s, 2p
(b) 4s, 3s, 3p, 4d
(c) 5p, 4d, 5d, 4f, 6s
(d) 5f, 6d, 7s, 7p
 
II. Based upon the above information, solve the questions given below :
(a) Which of the following orbitals has the lowest energy?
4d, 4f, 5s, 5p
(b) Which of the following orbitals has the highest energy?
5p, 5d, 5f, 6s, 6p

Answer:

I (a) (n+l) values are for 1s = 1 + 0 = 1, 2s = 2 + 0 = 2, 3s = 3 + 0 = 3, 2p = 2 + 1 = 3
Hence, increasing order of their energy is 1s<2s<2p<3s.

(b) 4s = 4 + 0 = 4, 3s = 3 + 0 = 3, 3p = 3 + 1 = 4, 4d = 4 + 2 = 6. Hence, 3s<3p<4s<4d.

(c) 5p = 5 + 1 = 6, 4d = 4 + 2 = 6, 5d = 5 + 2 = 7, 4f = 4 + 3 = 7, 6s = 6 + 0 = 6. Hence, 4d<5p<6s<4f<5d.

(d) 5f = 5 + 3 = 8, 6d = 6 + 2 = 8, 7s = 7 + 0 = 7, 7p = 7 + 1 = 8. Hence, 7s<5f<6d<7p.

II. (a) (n+l) values are for 4d = 4 + 2 = 6, 4f = 4 + 3 = 7, 5s = 5 + 0 = 5, 7p = 7+1 =8 . Hence, 5s has the lowest energy. 

     (b) 5p = 5 + 1 = 6, 5d = 5 + 2 = 7, 5f = 5 + 3 = 8, 6s = 6 + 0 = 6, 6p = 6 + 1 = 7. Hence, 5f has highest energy.
      

 

Page No 19:

Question 28:

Which of the following will not show deflection from the path on passing through an electric field?
Proton, cathode rays, electron, neutron.

Answer:

Charged particles can be disturbed by the presence of either electric or magnetic field.

Proton is a positively charged particle - so it will have deflection.

Cathode ray contains electrons that is negatively charged particle - so it will have deflection.

Electrons are negatively charged particle - so it will have deflection.

Neutron is electrically neutral - so will not have any deflection on the path.

Hence, Neutron will not have any deflection from the path on passing through an electric field.

Page No 19:

Question 29:

An atom having atomic mass number 13 has 7 neutrons. What is the atomic number of the atom?

Answer:

Atomic number of the atom = mass number - number of neutrons

As, mass number is given as 13 and number of neutrons is given is 7.

Therefore,  Atomic number = 13 - 7 = 6

Hence, the atomic number of the atom is 6.

Page No 19:

Question 30:

Wavelengths of different radiations are given below :
λ(A) = 300 nm
λ(B) = 300 μm 
λ(C) = 3 nm
λ(D) = 30 A°
Arrange these radiations in the increasing order of their energies.

Answer:

λ(A) = 300 nm, 300nm=300×109m=3×107m

λ(B) = 300 μm, 300μm=300×106m=3×104m

λ(C) = 3 nm, 3nm = 3×109m

λ(D) = 30 A°, 30Å=30×1010m=3×109m

As, E=hv=hcλ So, E1λ.
 Hence, increasing order of energy is 

 

Page No 19:

Question 31:

The electronic configuration of valence shell of Cu is 3d104s1 and not 3d94s2. How is this configuration explained?

Answer:

Configuration which have either half-filled or fully filled orbitals are more stable due to symmetrical distribution of electrons and maximum exchange energy in 3d104s1 d-orbitals are completely filled and s-orbital is half-filled. Hence it is more stable configuration.

Page No 19:

Question 32:

The Balmer series in the hydrogen spectrum corresponds to the transition from n1 = 2 to n2 = 3, 4, .........This series lies in the visible region. Calculate the wave number of line associated with the transition in Balmer series when the electron moves to n = 4 orbit.
(RH = 109677 cm–1)

Answer:

ν=_RH1n12-1n22 cm-1  = 109677122-142  = 20564.44 cm-1

Page No 19:

Question 33:

According to de Broglie, matter should exhibit dual behaviour, that is both particle and wave like properties. However, a cricket ball of mass 100 g does not move like a wave when it is thrown by a bowler at a speed of 100 km/h. Calculate the wavelength of the ball and explain why it does not show wave nature.

Answer:

Given mass of ball (m) = 100 g = 0.1 kg, given velocity of ball (v) = 100 km/h = 100 × 1000 m 60 × 60 s = 1000 m36 s
λ=hmv=6.626×1034kgm2s10.1kg×1000/36ms1=238.5×1036 m

As the wavelength of ball is very small, the wave nature cannot be detected.



Page No 20:

Question 34:

What is the experimental evidence in support of the idea that electronic energies in an atom are quantized?

Answer:

The bright line spectrum shows that the energy levels in an atom are quantized. These lines corresponds to definite wavelenghts and are obtained as a result of electronic transitions between the energy levels.
Hence, the electrons in these levels have quantized values.

Page No 20:

Question 35:

Out of electron and proton which one will have, a higher velocity to produce matter waves of the same wavelength? Explain it.

Answer:

The de-broglie equation states,  v=hmλ

The velocity here is inversely proportional on the masses.
Higher the mass lower will be the velocity. As, electron has lower mass than proton.
Hence, electron will have a higher velocity to produce matter waves of same wavelength.

Page No 20:

Question 36:

A hypothetical electromagnetic wave is shown in Fig. 2.2. Find out the wavelength of the radiation.

Answer:

Wavelength is defined as the distance between two successive peaks and two successive troughs of the wave.

Hence, the wavelength of the radiation would be λ=4×2.16 pm = 8.64 pm.
 

Page No 20:

Question 37:

Chlorophyll present in green leaves of plants absorbs light at 4.620 × 1014 Hz. Calculate the wavelength of radiation in nanometer. Which part of the electromagnetic spectrum does it belong to?

Answer:

Wavelength of light is given by the formula λ=hmv.

Given, frequency ν=4.620×1014 Hz=4.620×1014 s-1

λ=cν=3×1018 ms-14.620×1014 s-1 = 0.6494 × 10-6 m = 649.4 nm

Hence, wavelength of radiation in nanometer is 649.4 nm it belongs to visible region.
     

Page No 20:

Question 38:

What is the difference between the terms orbit and orbital?

Answer:

Difference between orbit and orbitals
              Orbit                 Orbital
Orbit is the circular path
in which electrons revolved
around the nucleus . 

This is the particular area, where probability of finding electrons is maximum . 
 Orbits are non -directional  They are directional , except , 's' orbital. 
In orbits , max. no of electrons in any orbit can be given by formula 2n2. The maximum numbers of electrons are always 2.

Page No 20:

Question 39:

Table-tennis ball has a mass 10 g and a speed of 90 m/s. If speed can be measured within an accuracy of 4% what will be the uncertainty in speed and position?

Answer:

Given that, speed = 90 m/s
Mass = 10 g = 10 × 10 −3 kg

Uncertainly in speed Δv=4×90100 = 36 m/s
From Heisenberg uncertainty principle Δx.Δvh4πm  
Δx=h4πmΔv = 6.626×1034 kgm2s14×3.14×10×103kg×3.6 ms1  = 1.46×10-33 m


 Hence, uncertainty in speed and position wold be 36 m/s and 1.46×10-33 m respectively.

Page No 20:

Question 40:

The effect of uncertainty principle is significant only for motion of microscopic particles and is negligible for the macroscopic particles. Justify the statement with the help of a suitable example.

Answer:

From Heisenberg uncertainty principle Δx.Δvh4πm  as the uncertainty is in inverse proportion with the mass we can say that greater mass will bring smaller in insignificant uncertainty for macroscopic particles.

If uncertainty principle is applied to an object of mass, say about a milligram (10−6 kg) then 

Δx.Δv=h4πm = 6.626×1034 kgm2s14×3.14×106kg  = 0.52 × 1028 m2s1

The value of  obtained is extremely small and is insignificant.

Therefore, for miligram-sized or heavier objects, the associated uncertainties are hardly of any real consequence.
 

Page No 20:

Question 41:

Hydrogen atom has only one electron, so mutual repulsion between electrons is absent. However, in multi-electron atoms mutual repulsion between the electrons is significant. How does this affect the energy of an electron in the orbitals of the same principal quantum number in multi-electron atoms?

Answer:

In case of hydrogen atom, the energies of the electron in different orbitals depends only on the value of n. Hence, different orbitals of the same shell have same energy. However, in case of multi electron atoms, the energies of the orbitals depend upon n+l values. Hence, for the same value of n but different value of l, i.e., different sub shells belonging to the same main shell have different energies.

Page No 20:

Question 42:

In some of the give question, one option of left column may be correlated to more than one option in the right column.
Match the following species with their corresponding ground state electronic configuration.
 

Atom / Ion  Electronic configuration
 (i) Cu  (a) 1s2 2s2 2p6 3s2 3p6 3d10
 (ii) Cu2+  (b) 1s2 2s2 2p6 3s2 3p6 3d10 4s2
 (iii) Zn2+  (c) 1s2 2s2 2p6 3s2 3p6 3d10 4s1
 (iv) Cr3+  (d) 1s2 2s2 2p6 3s2 3p6 3d9
   (e) 1s2 2s2 2p6 3s2 3p6 3d3


 

Answer:

The electronic configuration of the respective ions/element may be given as follows :

 (i) Electronic configuration of Cu =  2,8,18,1 i.e. 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹â° 4s¹

(ii) Electronic configuration of Cu²âº = 2,8,17 i.e. 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁹

(iii) Electronic Configuration of Zn²âº = 2,8,18,2 i.e. 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹â°

(iv) Electronic Configuration of Cr³âº = 2,8,8,3 i.e. 1s² 2s² 2p⁶ 3s² 3p⁶ 4d³

Hence, the correct matching of the electronic configuration is

 (i)  (c) ; (ii)  (d) ; (iii)  (a) ; (iv)  (e).

 



Page No 21:

Question 43:

In some of the given question, one option of left column may be correlated to more than one option in the right column.
Match the quantum numbers with the information provided by these.
 

Quantum number Information provided
 (i) Principal quantum number  (a) orientation of the orbital
 (ii) Azimuthal quantum number  (b) energy and size of orbital
 (iii) Magnetic quantum number  (c) Spin of the electron
 (iv) Spin quantum number  (d) shape of the orbital

Answer:

The correct match of quantum number with the provided information can be represented as follows:
 

Quantum number Information provided
(i) Principal quantum number (b) energy and size of orbital
(ii) Azimuthal quantum number (d) shape of the orbital
(iii) Magnetic quantum number (a) orientation of the orbital
(iv) Spin quantum number (c) Spin of the electron

Hence, the correct matching would be:

(i) with (b), (ii) with (d), (iii) with (a), (iv) with (c).

Page No 21:

Question 44:

In some of the given question, one option of left column may be correlated to more than one option in the right column.
Match the following rules with their statements :
 

Rules Statements
 (i) Hund’s Rule (a) No two electrons in an atom can have the same set of four quantum numbers.
(b) Half-filled and completely filled orbitals have extra stability.
 (ii) Aufbau Principle (c) Pairing of electrons in the orbitals belonging to the same subshell does not take place until each orbital is singly occupied.
 (iii) Pauli Exclusion Principle  (d) It is impossible to determine the exact position and exact momentum of a subatomic particle simultaneously.
 (iv) Heisenberg’s Uncertainty (e) In the ground state of atoms, orbitals are filled in the order of their increasing energies.

Answer:

The correct match of rules with the provided statements can be represented as follows:
 

Rules Statements
(i) Hund’s Rule (c) Pairing of electrons in the orbitals belonging to the same sub shell does not take place until each orbital is singly occupied.
(ii) Aufbau Principle (e) In the ground state of atoms, orbitals are filled in the order of their increasing energies.
(iii) Pauli Exclusion Principle (a) No two electrons in an atom can have the same set of four quantum numbers.
(iv) Heisenberg’s Uncertainty (d) It is impossible to determine the exact position and exact momentum of a subatomic particle simultaneously.

Hence, the correct matching would be:

(i) with (c), (ii) with (e), (iii) with (a), (iv) with (d).

Page No 21:

Question 45:

In some of the given question, one option of left column may be correlated to more than one option in the right column.
Match the following
 

 (i) X-rays
 (a) v = 10° – 104 Hz
 (ii) UV  (b) v = 1010 Hz
 (iii) Long radio waves  (c) v =1016 Hz
 (iv) Microwave  (d)v = 1018 Hz

Answer:

The correct match of Rays with the provided frequencies can be represented as follows:
 

Rays Frequency
(i) X-rays (d) = 1018 Hz
(ii) UV (c) v =1016 Hz
(iii) Long radio waves (a) = 10° – 10Hz
 (iv) Microwave (b) = 1010 Hz

Hence, the correct matching would be:

(i) with (d), (ii) with (c), (iii) with (a), (iv) with (b)



Page No 22:

Question 46:

In some of the given question, one option of left column may be correlated to more than one option in the right column.
Match the following

 (i) Photon
 (a) Value is 4 for N shell
 (ii) Electron  (b) Probability density
 (iii) ψ2  (c) Always positive value
 (iv) Principal quantum number n  (d) Exhibits both momentum and wavelength

Answer:

The correct match can be represented as follows:
 

(i) Photon (d) Exhibits both momentum and wavelength
(ii) Electron (d) Exhibits both momentum and wavelength
(iii) ψ2 (b) Probability density,  (c) Always positive value
(iv) Principal quantum number n (a) Value is 4 for N shell, (c) Always positive value

Hence, the correct matching would be:

(i) with (d), (ii) with (d), (iii) with (b) and (c), (iv) with (a) and (c). 

Page No 22:

Question 47:

In some of the given question, one option of left column may be correlated to more than one option in the right column.
Match species given in Column I with the electronic configuration given in Column II.
 

Column I Column II
 (i) Cr  (a) [Ar]3d84s0
 (ii) Fe2+  (b) [Ar]3d104s1
 (iii) Ni2+  (c) [Ar]3d64s0
 (iv) Cu  (d) [Ar] 3d54s1
   (e) [Ar]3d64s2

Answer:

The electronic configuration of the respective ions/element may be given as follows:
 

Column I Column II
(i) Cr (d) [Ar] 3d54s1
(ii) Fe2+ (c) [Ar]3d64s0
(iii) Ni2+ (a) [Ar]3d84s0
(iv) Cu (b) [Ar]3d104s1

Hence, the correct matching of the electronic configuration is (i) with (d), (ii) with (c), (iii) with (a), (iv) with (b).

Page No 22:

Question 48:

In the question a statement of Assertion (A) followed by a statement of Reason (R) is given. Choose the correct option out of the choices given below each question.
Assertion (A) : All isotopes of a given element show the same type of chemical behaviour.
Reason (R) : The chemical properties of an atom are controlled by the number of electrons in the atom.
(i) Both A and R are true and R is the correct explanation of A.
(ii) Both A and R are true but R is not the correct explanation of A.
(iii) A is true but R is false.
(iv) Both A and R are false.

Answer:

Both assertion and reason are true and reason is the correct explanation of assertion.
Isotopes have the same atomic number i.e. same number of electrons. Electrons are responsible for chemical behaviour of any element.
Therefore, isotopes exhibit similar chemical properties.
Hence, the correct answer is option A.

Page No 22:

Question 49:

In the question a statement of Assertion (A) followed by a statement of Reason (R) is given. Choose the correct option out of the choices given below each question.
Assertion (A) : Black body is an ideal body that emits and absorbs radiations of all frequencies.
Reason (R) : The frequency of radiation emitted by a body goes from a lower frequency to higher frequency with an increase in temperature.
(i) Both A and R are true and R is the correct explanation of A.
(ii) Both A and R are true but R is not the explanation of A.
(iii) A is true and R is false.
(iv) Both A and R are false.

Answer:

Both A and R are true and R is not the correct explanation of A .This can be explained as follows:
A body which absorbs and emits all radiations falling on it is called perfect black body. As temperature α frequency, with rise in temperature, frequency of radiation emitted by a body increases.

Hence, the correct answer is option B.



Page No 23:

Question 50:

In the question a statement of Assertion (A) followed by a statement of Reason (R) is given. Choose the correct option out of the choices given below each question.
Assertion (A) : It is impossible to determine the exact position and exact momentum of an electron simultaneously.
Reason (R) : The path of an electron in an atom is clearly defined.
(i) Both A and R are true and R is the correct explanation of A.
(ii) Both A and R are true and R is not the correct explanation of A.
(iii) A is true and R is false.
(iv) Both A and R are false.

Answer:

Assertion is true and reason is false. 
According to Heisenberg's uncertainly principle the exact position and exact momentum of an electron cannot be determined simultaneously. Thus, the path of electron in an atom is not clearly defined.

Hence, the correct answer is option C.

Page No 23:

Question 51:

What is photoelectric effect? State the result of photoelectric effect experiment that could not be explained on the basis of laws of classical physics. Explain this effect on the basis of quantum theory of electromagnetic radiations.

Answer:

When radiation with certain minimum frequency v0 strike the surface of a metal, electrons are ejected from the surface of the metal this phenomenon is called photoelectric effect. 
 
Experiment showing photoelectric effect:

Light of a particular frequency strikes a clean metal surface inside a vacuum chamber. Electrons are ejected from the metal and are counted by a detector that measures their kinetic energy.

The result observed in this experiment were:
 
(i) The electrons are ejected from the metal surface as soon as the beam of light strikes the surface. i.e. there is no time lag between the striking of light beam and the ejection of electrons from the metal surface. 
(ii) The number of electrons ejected is proportional to the intensity or brightness of light. 
(iii) For each metal, there is a characteristic minimum frequency, v0 (also known as threshold frequency) below which photoelectric effect is not observed. At a frequency v>v0 the ejected electrons come out with certain kinetic energy. The kinetic energies of these ejected electrons increases with the increase of frequency of the light used.

The above observation cannot be explained by the electromagnetic wave theory. According to this theory, since radiations were continuous therefore, it should be possible to accumulate energy on the surface of the metal irrespective of it frequency and thus, radiations of all frequencies should be able to eject electrons. 
Similarly according to this theory the energy of the electrons ejected should depend upon the intensity of the incident radiation. 

Particle Nature of Electromagnetic Radiation 
To explain the phenomena of black body radiation and photoelectric effect Max planck in 1900, put forward a theory known after his name as Planck's quantum theory. This theory was further extended by Einstein in 1905. 

(i) The radiant energy is emitted or absorbed not continuously but discontinuously in the form of small discrete packets of energy each such packet of energy is called a quantum, in case of light quantum of energy is called a photon. 
(ii) The energy of each quantum is directly proportional to the frequency of the radiation 
i.e. E α ν or E = hv.
where h is a proportionality constant called planck's constant. Its value to approximately equal to 6.626×10−34 Js. 
(iii) The total amount of energy emitted or absorbed by a body will be some whole number quanta. 
Hence,E = nhv (where, n is any integer).

Page No 23:

Question 52:

Threshold frequency, v0 is the minimum frequency which a photon must possess to eject an electron from a metal. It is different for different metals. When a photon of frequency 1.0 × 1015 s–1 was allowed to hit a metal surface, an electron having 1.988 × 10–19 J of kinetic energy was emitted. Calculate the threshold frequency of this metal. Show that an electron will not be emitted if a photon with a wavelength equal to 600 nm hits the metal surface.

Answer:

We know, hν= hv0 + K.E.

v = 1.0 × 1015 s–1 , K.E. = 1.988 × 10–19 J , 6.626×10-34 Js 

v0 = 1.0 × 1015 s1  1.988 × 1019 J  6.626 × 1034 Js = 7.0×1014 s-1 Hz 

Frequency of striking photon may be calculated as follows : 

ν=cλ = 3.0×108 ms1600×109 m = 5.0×1014 s1 Hz

Since the frequency of the striking photon is less than the threshold frequency, an electron will, not be emitted from the metal surface under the influence of the influence of the striking photon.


 

Page No 23:

Question 53:

When an electric discharge is passed through hydrogen gas, the hydrogen molecules dissociate to produce excited hydrogen atoms. These excited atoms emit electromagnetic radiation of discrete frequencies which can be given by the general formula v=1096771nt2-1nf2
What points of Bohr’s model of an atom can be used to arrive at this formula? Based on these points derive the above formula giving description of each step and each term.

Answer:

Two important points of Bohr's model that can be used to derive the given formula are: 
(i) Electrons revolve around the nucleus in stationary states i.e. orbits with fixed values of energy (quantized values). 
(ii) Energy is emitted or absorbed only when electron jumps from one orbit to another.

Derivation:
Step (i) The energy of the electron in the nth stationary state is given by : En= 2π2me4n2h2
where m = mass of electron, e = charge on electron, h = Planck's constant.

Step (ii) When the electron jumps from outer stationary state nto inner stationary state n1 the different of energy (ΔE) is emitted i.e.ΔE=E2E1 = 2π2me4h2 (1n121n22) 

​Step (iii), ΔE = hν = hcλ 

1λ=ΔEhc=2π2me4ch3 (1n12 - 1n22) 

Substituting the value of the constant, π,m,e in C.G.S units, we get:
1λ = 109677 cm-1  (1n12 - 1n22) 

1λ=v¯  which is also called as wave number 

Therefore, v¯ = 1λ = 109677 cm-1  (1n12 - 1n22) 
 

Page No 23:

Question 54:

Calculate the energy and frequency of the radiation emitted when an electron jumps from n = 3 to n = 2 in a hydrogen atom.

Answer:

In hydrogen spectrum the spectral lines are expressed in term of wave number 1λ = v¯ obey the following formula :

v ¯= 1λ = 109677 cm-1  (1n12 - 1n22)  

v ¯ = 109677 cm-1  (122 - 132)  = 109677 × 536 = 15232 cm1

λ = 6.564 × 105 cm =  6.564×107m 

E = hcλ = 6.626 × 1034 Js × 30 × 108 ms16.564 × 107 m = 3.028 × 10−19 J

ν = cλ = 3.0 × 108 ms1 6.564 × 107m  = 0.457 × 1015 s1

Hence, the energy is 3.028 × 10−19 J and frequency is  0.457 × 1015 s1.

Page No 23:

Question 55:

Why was a change in the Bohr Model of atom required? Due to which important development (s), concept of movement of an electron in an orbit was replaced by, the concept of probability of finding electron in an orbital? What is the name given to the changed model of atom?

Answer:

Bohr Model atom suffered from certain limitations :

1) According to Bohr, the radiation results when an electron jumps from one energy orbit to another energy orbit, but how this radiation occurs is not explained by Bohr.
2) Bohr Theory had explained the existence of various lines in H-spectrum, but it predicted that only a series of lines exist. At that time this was exactly what had been observed. However, as better instruments and techniques were developed, it was realized that the spectral line that had been thought to be a single line was actually a collection of several lines very close together (known as fine spectrum). 
3) Thus the appearance of the several lines implies that there are several energy levels, which are close together for each quantum number   n. This would require the existence of new quantum numbers.
4) Bohr's theory has successfully explained the observed spectra for hydrogen atom and hydrogen like ions (e.g. He+, Li2+, Be3+ etc), it can not explain the spectral series for the atoms having a large number of electrons.
5) There was no satisfactory justification for the assumption that the electron can rotate only in those orbits in which the angular momentum of the electron (mvr) is a whole number multiple of h/2π, i.e. he could not give any explanation for using the principle of quantisation of angular momentum and it was introduced by him arbitrarily.
6) Bohr assumes that an electron in an atom is located at a definite distance from the nucleus and is revolving round it with definite velocity, i.e. it is associated with a fixed value of momentum. This is against the Heisenberg's Uncertainty Principle according to which it is impossible to determine simultaneously with certainty the position and the momentum of a particle.
7) No explanation for Zeeman effect: If a substance which gives a line emission spectrum, is placed in a magnetic field, the lines of the spectrum get split up into a number of closely spaced lines. This phenomenon is known as Zeeman effect. Bohr's theory has no explanation for this effect.
8) No explanation of the Stark effect: If a substance which gives a line emission spectrum is placed in an external electric field, its lines get split into a number of closely spaced lines. This phenomenon is known as Stark effect. Bohr's theory is not able to explain this observation as well.

The concept of the movement of an electron in an orbit was no longer considered to be proper. The concept of probability of finding the electron in an atom was based upon Heiseberg's Uncertainty principle. The modified model of atom is known as quantum mechanical  model.



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