3 + Interview Questions in GENERAL QA IN ATOMS Page 1 InterviewSolution

1.	The ground state energy of hydrogen atom is −13.6 eV. What are the kinetic and potential energies of the electron in this state?
Answer» Ground state energy of hydrogen atom, E = − 13.6 eV This is the total energy of a hydrogen atom. Kinetic energy is equal to the negative of the total energy. Kinetic energy = − E = − (− 13.6) = 13.6 eV Potential energy is equal to the negative of two times of kinetic energy. Potential energy = − 2 × (13.6) = − 27 .2 eV

1.

The ground state energy of hydrogen atom is −13.6 eV. What are the kinetic and potential energies of the electron in this state?

Answer»

Ground state energy of hydrogen atom, E = − 13.6 eV

This is the total energy of a hydrogen atom. Kinetic energy is equal to the negative of the total energy.
Kinetic energy = − E = − (− 13.6) = 13.6 eV
Potential energy is equal to the negative of two times of kinetic energy. Potential energy = − 2 × (13.6) = − 27 .2 eV

Discussion

2.	Answer the following questions, which help you understand the difference between Thomson’s model and Rutherford’s model better. (a) Is the average angle of deflection of α-particles by a thin gold foil predicted by Thomson’s model much less, about the same, or much greater than that predicted by Rutherford’s model?(b) Is the probability of backward scattering (i.e.,scattering of α-particles at angles greater than 90°) predicted by Thomson’s model much less, about the same, or much greater than that predicted by Rutherford’s model?(c) Keeping other factors fixed, it is found experimentally that for small thickness t, the number of α-particles scattered at moderate angles is proportional to t. What clue does this linear dependence on t provide?(d) In which model is it completely wrong to ignore multiple scattering for the calculation ofaverage angle of scattering of α-particles by a thin foil?
Answer» (a) about the same The average angle of deflection of α-particles by a thin gold foil predicted by Thomson’s model is about the same size as predicted by Rutherford’s model. This is because the average angle was taken in both models. (b) much less The probability of scattering of α-particles at angles greater than 90° predicted by Thomson’s model is much less than that predicted by Rutherford’s model. (c) Scattering is mainly due to single collisions. The chances of a single collision increases linearly with the number of target atoms. Since the number of target atoms increase with an increase in thickness, the collision probability depends linearly on the thickness of the target. (d) Thomson’s model It is wrong to ignore multiple scattering in Thomson’s model for the calculation of average angle of scattering of α−particles by a thin foil. This is because a single collision causes very little deflection in this model. Hence, the observed average scattering angle can be explained only by considering multiple scattering.

2.

Answer the following questions, which help you understand the difference between Thomson’s model and Rutherford’s model better. (a) Is the average angle of deflection of α-particles by a thin gold foil predicted by Thomson’s model much less, about the same, or much greater than that predicted by Rutherford’s model?(b) Is the probability of backward scattering (i.e.,scattering of α-particles at angles greater than 90°) predicted by Thomson’s model much less, about the same, or much greater than that predicted by Rutherford’s model?(c) Keeping other factors fixed, it is found experimentally that for small thickness t, the number of α-particles scattered at moderate angles is proportional to t. What clue does this linear dependence on t provide?(d) In which model is it completely wrong to ignore multiple scattering for the calculation ofaverage angle of scattering of α-particles by a thin foil?

Answer»

(a) about the same

The average angle of deflection of α-particles by a thin gold foil predicted by Thomson’s model is about the same size as predicted by Rutherford’s model. This is because the average angle was taken in both models.
(b) much less

The probability of scattering of α-particles at angles greater than 90° predicted by Thomson’s model is much less than that predicted by Rutherford’s model.
(c) Scattering is mainly due to single collisions. The chances of a single collision increases linearly with the number of target atoms. Since the number of target atoms increase with an increase in thickness, the collision probability depends linearly on the thickness of the target.
(d) Thomson’s model

It is wrong to ignore multiple scattering in Thomson’s model for the calculation of average angle of scattering of α−particles by a thin foil. This is because a single collision causes very little deflection in this model. Hence, the observed average scattering angle can be explained only by considering multiple scattering.

Discussion

3.	Choose the correct alternative from the clues given at the end of the each statement:(a) The size of the atom in Thomson’s model is .......... the atomic size in Rutherford’smodel. (much greater than/no different from/much less than.)(b) In the ground state of .......... electrons are in stable equilibrium, while in ..........electrons always experience a net force.(Thomson’s model/ Rutherford’s model.)(c) A classical atom based on .......... is doomed to collapse.(Thomson’s model/ Rutherford’s model.)(d) An atom has a nearly continuous mass distribution in a .......... but has a highlynonuniform mass distribution in ..........(Thomson’s model/ Rutherford’s model.)(e) The positively charged part of the atom possesses most of the mass in ..........(Rutherford’s model/both the models.)
Answer» (a) The sizes of the atoms taken in Thomson’s model and Rutherford’s model have the same order of magnitude. (b) In the ground state of Thomson’s model, the electrons are in stable equilibrium. However, in Rutherford’s model, the electrons always experience a net force. (c) A classical atom based on Rutherford’s model is doomed to collapse. (d) An atom has a nearly continuous mass distribution in Thomson’s model, but has a highly non-uniform mass distribution in Rutherford’s model. (e) The positively charged part of the atom possesses most of the mass in both the models.

Discussion

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The ground state energy of hydrogen atom is −13.6 eV. What are the kinetic and potential energies of the electron in this state?