WS ON ATOMS
1. Define the term impact parameter
2. Derive an expression for the total energy of an electron in a hydrogen atom?
3. Derive an expression for the total energy of an electron in the nth orbit of a hydrogen
atom?
4. The short wavelength limit for Lyman series of the hydrogen spectrum is 913.4A°.
Calculate the short wavelength limit for Balmer series of the hydrogen spectrum.
5. The ground state of hydrogen atom is -13.6eV. If an electron makes a transition from an
energy level -1.51eV to -3.4eV, calculate the of the spectral line emitted and name the
series of hydrogen spectrum to which it belongs.
6. a) The energy levels of a hypothetical hydrogen- like atom are shown in the figure.
Find out the transition, from the ones shown in the figure, which will result in the
emission of a photon of wavelength 275 nm.
b) Which of these transitions corresponds to the emission of radiation of maximum
wavelength and minimum wavelength?
7. 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?
8. Find the ratio of energies of photons produced due to transition of an electron of hydrogen
atom from its
1. Second permitted energy level to the first level and
2. Highest permitted energy level to the first permitted level
9.
The electron in a given Bohr orbit has a total energy of –1.5 eV. Calculate its
a) kinetic energy
b) potential energy
c) wavelength of radiation emitted, when this electron makes a transition to the
ground state. [Given : Energy in the ground state = –13.6 eV and Rydberg’s
constant = 1.09 × 107 m–1]
10. A 12.5eV electron beam is used to excite a gaseous hydrogen atom at room temperature.
Determine the wavelengths and the corresponding series pf lines emitted.
11. Find out the wavelength of the electron orbiting in the ground state of hydrogen atom.
12. The value of ground state energy of hydrogen atom is -136. eV.
(i) Find the energy required to move an electron from the ground state to the first
excited state of the atom.
(ii) (ii) Determine (a) the kinetic energy and (b) orbital radius in the first excited
state of the atom. (Given, the value of Bohr's radius= 053. Å)
13. (a) In Geiger-Marsden experiment, calculate the distance of closest approach for an alpha
particle with energy 2·56 10 12 J. Consider that the particle approaches gold nucleus (Z =
79) in head-on position. (b) If the above experiment is repeated with a proton of the same
energy, then what will be the value of the distance of closest approach ?
