Sure Shot Questions 2025

Chapter – 12
Atoms
➢ Questions 8. State Bohr’s quantization condition of angular
momentum. Calculate the shortest wavelength of
the Brackett series and state to which part of the
1. A proton of energy 1.6 MeV approaches a gold electromagnetic spectrum does it belong.
nucleus (Z = 79). Find the distance of its closest
approach. 9. The ground state energy of hydrogen atom is -13.6
eV. If an electron makes a transition from an
2. Using Bohr's postulates, derive the expression energy level -1.51 eV to -3.4 eV, calculate the
wavelength of the spectral line emitted and name
for the radius of the 𝑛𝑡ℎ orbit of an electron in a
the series of hydrogen spectrum to which it
hydrogen atom. Also, find the numerical value of
belongs.
Bohr's radius 𝑎0

3. What result do you expect if  -particle scattering 10. The short wavelength limit for the Lyman series of
0
experiment is repeated using a thin sheet hydrogen the hydrogen spectrum is 913.4 A . Calculate the
in place of a gold foil? Explain. (Hydrogen is a solid short wavelength limit for the Balmer series of the
at temperature below 14K) hydrogen spectrum.

4. Define the distance of closest approach. An  -

11. (a) In Geiger – Marsden experiment, calculate the
particle of kinetic energy ‘K’ is bombarded on a
distance of closest approach for an alpha particle
thin gold foil. The distance of the closest approach
with energy 2.56 x 10-12 J. Consider that the
is ‘r’. What will be the distance of closest approach
particle approaches gold nucleus (Z = 79) in head –
for an  -particle of double the kinetic energy?
on position. (b) If the above experiment is
repeated with a proton of the same energy, then
5. Write two important limitations of Rutherford
what will be the value of the distance of closest
nuclear model of the atom.
approach?
6. Using Bohr’s atomic model, derive the expression
for the radius of nth orbit of the revolving electron 12. A hydrogen atom initially in the ground state
in a hydrogen atom. absorbs a photon which excites it to the n = 4 level.
OR Estimate the frequency of the photon.
Show that the radius of the orbit in hydrogen
atom varies as n2, where n is the principal 13. A 12.5 eV electron beam is used to bombard
quantum number of the atom. gaseous hydrogen at room temperature. Upto
OR which energy level the hydrogen atoms would be
Using Bohr’s postulates of the atomic model, excited?
derive the expression for the radius of nth Calculate the wavelengths of the first member of
electron orbit. Hence obtain the expression for Lyman and first member of Balmer series.
Bohr’s radius.
14. Calculate the de-Broglie wavelength associated
7. Write shortcomings of Rutherford atomic model. with the electron in the 2nd excited state of
Explain how these were overcome by the hydrogen atom. The ground state energy of the
postulates of Bohr’s atomic model. hydrogen atom is 13.6 eV.

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15. Derive an expression for the frequency of radiation
emitted when a hydrogen atom de-excites from
level n to level (n – 1). Also show that for large
values of n, this frequency equals to classical
frequency of revolution of an electron.

16. (a) Write two important limitations of Rutherford 24. Using Bohr’s postulates, obtain the expression for
model which could not explain the observed the total energy of the electron in the stationary
features of atomic spectra. How were these states of the hydrogen atom. Hence draw the
explained in Bohr’s model of hydrogen atom? energy level diagram showing how the line spectra
(b) Using Bohr’s postulates, obtain the expression corresponding to Balmer series occur due to
for the radius of the nth orbit in hydrogen atom. transition between energy levels.

17. Using Bohr’s postulates, derive the expression for 25. The ground state energy of hydrogen atom is
the total energy of the electron in the secondary −13.6 𝑒𝑉. If an electron makes a transition from an
states of the hydrogen atom. energy level −1.51 𝑒𝑉 to −3.4 𝑒𝑉 , calculate the
wavelength of the spectral line emitted and the
series of hydrogen spectrum to which it belongs.
18. State the basic assumption of the Rutherford
model of the atom. Explain, in brief, why this
26. Write two important limitations of Rutherford
model cannot account for the stability of an atom.
nuclear model of the atom.
19. State Bohr’s quantization condition of angular
27. Define the distance of closest approach. An 𝛼-
momentum. Calculate the shortest wavelength of
particle of kinetic energy ‘K’ is bombarded on a thin
the Brackett series and state to which part of the
gold foil. The distance of the closest approach is ‘r’.
electromagnetic spectrum does it belong.
What will be the distance of closest approach for
an𝛼-particle of double the kinetic energy?
20. A hydrogen atom in the ground state is excited by
an electron beam 12.5 eV energy. Find out the 28. The electron, in a hydrogen atom, is in its second
maximum number of lines emitted by atom from its excited state.
excited state. Calculate the wavelength of the lines in the Lyman
series that can be emitted through the permissible
transitions of this electron. [Given the value of
21. How is the stability of hydrogen atom in Bohr model Rydberg constant, R = 1.1 x 107 m-1]
explained by de-Broglie’s Hypothesis?
29. The energy level diagram of an element is given
22. (a) Draw the energy level diagram for the line below. Identify, by doing necessary calculations,
spectra representing Lyman series and Balmer which transition corresponds to the emission of a
series in the spectrum of hydrogen atom. spectral line of wavelength 102.7 nm.
(b) Using the Rydberg formula for the spectrum of
hydrogen atom, calculate the largest and shortest
wavelengths of the emission lines of the Balmar
series in the spectrum of hydrogen atom. (Use the
value of Rydberg constant 𝑅 = 1.1 × 107 𝑚−1 .

23. (a) state Bohr’s quantization condition for defining

stationary orbits. How does de-Broglie hypothesis 30. (i) The radius of the innermost electron orbit of a
explain the stationary orbits? hydrogen atom is 5.3 x 10-11 m. Calculate its radius
(b)Find the relation between the three wavelengths in n = 3 orbit.
𝜆1 , 𝜆2 𝑎𝑛𝑑 𝜆3 from the energy level diagram shown (ii) The total energy of an electron in the first
below. excited state of the hydrogen atom is −3.4 𝑒𝑉. Find
out its (a) kinetic energy and (b) Potential energy in
this state.

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31. Using Bohr's second postulate of quantization of (b) The electron in a given Bohr orbit has a total
orbital angular momentum show that the energy of −1.5 𝑒𝑉. Calculate its
circumference of the electron in the orbital state in (i) kinetic energy.
hydrogen atom is n times the de-Broglie (ii) potential energy.
wavelength associated with it. (iii) wavelength of radiation emitted, when this
electron makes a transition to the ground state.
32. (a) Explain Bohr's quantization condition of angular [Given: Energy in the ground state = −13.6 𝑒𝑉 and
momentum. Rydberg's constant = 1.09 × 107 𝑚−1 ]

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