11/20/24, 6:17 AM Test Generator
Roll No. : Time -
Date : MM - 68
1. A proton strikes another proton at rest. Assume impact-parameter to be zero, i.e. head-on 2
collsion. How close will the incident proton go to other proton?
2. Find the ionization energy and ionization potential of ground state electron in hydrogen atom. 2
3. What is the angular momentum of an electron in Bohr’s hydrogen atom whose energy is –3.4 2
eV?
4. What is the difference between Rutherford and Bohr’s model? 2
5. Draw a labelled diagram of Geiger and Marsden experiment on α-particle scattering. Explain how 2
does it help to find the size of a nucleus.
6. State Bohr’s postulate of hydrogen atom which successfully explains the emission lines in the 2
spectrum of hydrogen atom.
Use Rydberg formula to determine the wavelength of Ha line.
[Given: Rydberg constant R = 1.09 × 107 m–1]
7. Using Rutherford model of the atom, derive the expression for the total energy of the electron in 2
hydrogen atom. What is the significance of total negative energy possessed by the electron?
8. Define ionization energy. How would the ionization energy change when electron in a hydrogen 2
atom is replaced by a particle of mass 200 times that of the electron but having the same charge?
9. An electron during its transition from second excited state to ground state emits the radiation of 2
wavelength λ. Answer the following:
(a) In which series of transition this emission lies?
(b) Name the region of em wave spectrum.
10. An atom absorbs a photon of wavelength λ and then re-emits the energy in two steps. If one 2
emitted wavelength is 3 λ, what will be the other wavelength?
11. Determine the ratio of distance of closest approach of a proton and an alpha particle incident on 2
a thin gold foil, if they have same kinetic energy.
12. Define the distance of closest approach. An a-particle of kinetic energy ‘K’ is bombarded on a 2
thin gold foil. The distance of the closest approach is ‘r’. What will be the distance of closest
approach for an a-particle of double the kinetic energy?
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11/20/24, 6:17 AM Test Generator
13. State Bohr’s quantization condition of angular momentum. Calculate the shortest wavelength of 2
the Bracket series and state to which part of the electromagnetic spectrum does it belong.
14. In an experiment on α-particle scattering by a thin foil of gold, draw a plot showing the number of 3
particles scattered versus the scattering angle θ. Why is it that a very small fraction of the particles
are scattered at θ > 90°?
Write two important conclusions that can be drawn regarding the structure of the atom from the
study of this experiment.
15. Consider energy level diagram of a hydrogen atom. How will the kinetic energy and potential 3
energy of electron vary if the electron moves from a lower level to a higher level?
16. Using Bohr’s postulates for hydrogen atom, show that the total energy (E) of the electron in the 3
stationary states can be expressed as the sum of kinetic energy (K) and potential energy (U),
where K = – U. Hence deduce the expression for the total energy in the nth energy level of
hydrogen atom.
17. Using Bohr’s postulates, obtain the expression for the total energy of the electron in the 3
stationary states of the hydrogen atom. Hence draw the energy level diagram showing how the line
spectra corresponding to Balmer series occur due to transition between energy levels.
18. Using the postulates of Bohr’s model of hydrogen atom, obtain an expression for the frequency 3
of radiation emitted when the atom makes a transition from the higher energy state with quantum
number ni to the lower energy state with quantum number nf (nf < ni).
19. (a) Using Bohr’s second postulate of quantization of orbital angular momentum show that the 3
circumference of the electronic in the nth orbital state in hydrogen atom is n times the de Broglie
wavelength associated with it.
(b) The electron in hydrogen atom is initially in the third excited state. What is the maximum number
of spectral lines which can be emitted when it finally moves to the ground state?
20. (a) Using postulates of Bohr’s theory of hydrogen atom, show that 3
2
(i) the radii of orbits increases as n , and
(ii) the total energy of the electron increases as 1/n2, where n is the principal quantum number of
the atom.
(b) Calculate the wavelength of Hα line in Balmer series of hydrogen atom, given Rydberg’s
constant R = 1.0947 × 107 m–1.
21. Using Bohr’s postulates, obtain the expressions for (i) kinetic energy and (ii) potential energy of 3
the electron in stationary state of hydrogen atom.
Draw the energy level diagram showing how the transitions between energy levels result in the
appearance of Lyman series.
22. (a) The energy levels of a hypothetical hydrogen-like atom are shown in the figure. Find out the 3
transition, from the ones shown in the figure, which will result in the emission of a photon of
wavelength 275 nm.
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11/20/24, 6:17 AM Test Generator
(b) Which of these transitions corresponds to the emission of radiation of (i) maximum and (ii)
minimum wavelength?
23. 3
If the energy of an electron in H-atom is Then using above expression show that (a)
an electron cannot have energy of – 2V. (b) spacing between energy levels decreases as n
increases.
24. Write shortcomings of Rutherford atomic model. Explain how these were overcome by the 3
postulates of Bohr’s atomic model.
25. Using Bohr’s postulates, derive the expression for the orbital period of the electron moving in the 3
nth orbit of hydrogen atom.
26. (a) State Bohr’s postulate to define stable orbits in hydrogen atom. How does de Broglie’s 3
hypothesis explain the stability of these orbits?
(b) A hydrogen atom initially in the ground state absorbs a photon which excites it to the n = 4 level.
Estimate the frequency of the photon.
27. (a) How did de Broglie hypothesis provide an explanation for Bohr’s second postulate for 3
quantisation of orbital angular momentum of the orbiting electron in hydrogen atom? Discuss.
(b) Identify the transition of electron in Bohr model which gives rise to (i) the maximum, and (ii) the
minimum wavelength in Balmer series of hydrogen spectrum.
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