Kuwait University
Faculty of Science
Physics Department
Modern Physics 209
Final Examination
Date: January 2004
Time: 2 Hours
Instructors: Drs. K.S. Bhatia & Abdulmuhsen Ali
Name……………………………….. Student No. …………
1.
2.
Do any 7 problems
Show detailed solution for each problem
Prob.
Marks
1
2
3
4
5
6
7
Total
1.
Prove the following equations:
Total energy E of mass m is
E = mc2
c is the velocity of light.
momentum p =
1
E - moc 2
c
2. A and B are twin brothers of 10 year age. A makes a round trip to a
galaxy 100 Light years away with a speed of 0.85 C, while B remains
on the earth. W hat is the age difference between A and B when they
meet again?
3.
X-rays of  = 0.2 nm are scattered from carbon block. Binding energy
of the electron in carbon atom is 4 eV. Calculate the
a)
b)
Energy of the scattered photon at 45.
The corresponding angle and momentum of the scattered
electron.
4.
A laser light of  300 nm and intensity 1 mw/cm2 falls on 1cm2 of a
photosensitive surface ( workfunction = 2 eV). Calculate the velocity of
emitted electrons and the current generated by the photo surface.
(Assume each photon releases one photoelectron).
5.
An electron trapped in an infinite potential well of length 0.1 nm
transfers from 3rd energy state to 1st energy state and it radiates the
energy in the form of electromagnetic wave. Calculate the wavelength of
the radiation.
6.
A hydrogen atom in an excited state emits wavelength of  = 102.5 nm
when the electron returns to the ground state. Calculate the principle
quantum number n for the excited state.
7.
A hydrogen atom is 5.3  10-11 m in radius. Use uncertainty principle to
estimate minimum energy an electron can have in this atom. W hat is the
actual value for lowest energy of an electron in hydrogen atom.
8.
9.
Calculate all the angles of L vector with the z vector for the orbital
quantum
Number  = 2.
Show that the radial probability density of the 1s level has its maximum
Value at r = ao
(Hint: Radial wavefunction for 1s = ( 2/ao3/2 ) e-r/a and radial probability
is given by P(r) = r2 | Rn (r) | 2