PHYSICS: Xll Atoms

PREVIOUS YEARS QUESTIONS ATOMS

1) O2 molecule consists of two oxygen atoms. In the molecule, nuclear force between the nuclei of the two atoms
a) is not important because nuclear forces are short-ranged.
b) is as important as electrostatic force for binding the two atoms.
c) cancels the repulsive electrostatic force between the nuclei.
d) is not important because oxygen nucleus have equal number of neutrons and protons.

2) A set of atoms in an excited state decays.

a) in general, to any of the states with lower energy.
b) into a lower state only when excited by an external electric field.
c) all together simultaneously into a lower state.
d) to emit photons only when they collide.

3) Two H atoms in the ground state collide inelastically. The maximum amount by which their combined kinetic
energy is reduced is:
(a) 10.20 eV (b) 20.40 eV (c) 13.6 eV (d) 27.2 eV.

4) For the ground state, the electron in the H-atom has an angular momentum = h, according to the simple Bohr
model. Angular momentum is a vector and hence there will be infinitely many orbits with the vector pointing in all
possible directions. In actuality, this is not true,
a) because Bohr model gives incorrect values of angular momentum.
b) because only one of these would have a minimum energy.
c) angular momentum must be in the direction of spin of electron.
d) because electrons go around only in horizontal orbits.

5) Taking the Bohr radius as a0 = 53 pm, the radius of Li++ ion in its ground state, on the basis of Bohr’s model, will
be about
(a) 53 pm. (b) 27 pm. (c) 18 pm. (d) 13 pm.

6) The binding energy of a H-atom, considering an electron moving around a fixed nuclei (proton), is
 me 4
B (m = electron mass). If one decides to work in a frame of reference where the electron is at
8n 2 0 h 2
2

rest, the proton would be moving around it. By similar arguments, the binding energy would be
 Me4
B (M= proton mass) This last expression is not correct because:
8n 2 0 h 2
2

a) n would not be integral

b) Bohr-quantisation applies only to electron
c) the frame in which the electron is at rest is not inertial.
d) the motion of the proton would not be in circular orbits, even approximately.

7) Choose the correct alternative from the clues given at the end of each statement :
a) The size of the atom in Thomson’s model is .......... the atomic size in Rutherford’s model. (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 . ............ but has a highly non uniform 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)

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PHYSICS: Xll Atoms

SECTION B

1) When is H  line of the Balmer series in the emission spectrum of hydrogen atom obtained?
2) What is the maximum number of spectral lines emitted by a hydrogen atom when it is in the third excited state?
3) What is the maximum number of spectral lines emitted by a hydrogen atom when it is in the fourth excited state?
4) Define the distance of closest approach. An  -particle of kinetic energy ‘K’ is bombarded on a thin gold foil.
The distance of the closest approach is ‘r’. What will be the distance of closest approach for an  - particle of
double the kinetic energy?
5) Write two important limitations of Rutherford nuclear model of the atom.
6) The ground state energy of hydrogen atom is – 13.6 eV. If an electron makes a transition from an 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.
7) Define ionization energy. How would the ionization energy change when electron in hydrogen atom is replaced
by the particle of mass 200 times that of the electron but having the same charge?
[Given Rydberg constant, R = 107 m–1]
8) Calculate the ratio of the frequencies of the radiation emitted due to transition of the electron in a hydrogen atom
from its (i) second permitted energy level to the first level and (ii) highest permitted energy level to the second
permitted level
9) Calculate the shortest wavelength of the spectral lines emitted in Balmer series.
(Given Rydberg constant, R = 107 m–1)
10) In the ground state of hydrogen atom, its Bohr radius is given as 5.3 × 10 –11 m. The atom is excited such that the
radius becomes 21.2 × 10–11 m. Find (i) the value of the principal quantum number and (ii) the total energy of the
atom in this excited state.

11) The energy levels of a hypothetical atom are given below.

Which of the shown transitions will result in the emission of
photon of wavelength 275 nm?

12) Calculate the de-Broglie wavelength of the electron orbiting in the n = 2 state of hydrogen atom.
13) Show that the radius of the orbit in hydrogen atom varies as n 2 , where n is the principal quantum number of the
atom
14) The electron, in a hydrogen atom, is in its second 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
Rydberg constant, R = 1.1 × 107 m–1)
15) An  -particle moving with initial kinetic energy K towards a nucleus of atomic number Z approaches a
distance ‘d’ at which it reverses its direction. Obtain the expression for the distance of closest approach
‘d’ in terms of the kinetic energy of  -particle K
16) Find the ratio between the wavelengths of the ‘most energetic’ spectral lines in the Balmer and Paschen series of
the hydrogen spectrum.
17) Using Rutherford model of the atom, derive the expression for the total energy of the electron in hydrogen atom.
What is the significance of total negative energy possessed by the electron?

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PHYSICS: Xll Atoms

18) The short wavelength limit for the Lyman series of the hydrogen is 913.4 Å. Calculate the short wavelength limit
for Balmer series of hydrogen spectrum.
19) Using Bohr’s postulates, derive the expression for the orbital period of the electron moving in the n th orbit of
hydrogen atom.
20) State Bohr’s quantization condition for defining stationary orbits.
How does de-Broglie hypothesis explain the stationary orbits? Find
the relation between the three wavelengths 1 ,  2 and 3 from the
energy level diagram shown below.

21) Draw a schematic arrangement of Geiger-Marsden experiment

showing the scattering of  -particles by a thin foil of gold. Why is it that most of the  -particles go right
through the foil and only a small fraction gets scattered at large angles?

22) Draw the trajectory of the  -particle in the coulomb field of a nucleus. What is the significance of impact
parameter and what information can be obtained regarding the size of the nucleus?

23) Estimate the distance of closest approach to the nucleus (Z = 80) if a 7.7 MeV  -particle before it comes
momentarily to rest and reverses its direction.

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