Problem 1. Calculate for He+ (i) radius of the first Bohr orbit, (ii) velocity of electron moving in first, (iii) orbital frequency in the first orbit, (io) kinetic energy and binding energy of electron in the grond state, (v) ionization potential and the first excitation potential, and (vi) wavelength of the resonance line emitted in the transition n = 2 → n = 1.
Solution: (i) For helium atom Z = 2
(i) For 2P3/2 state, L = 1, S = ½, J = 3/2 ⇒ g = 4/3
(ii) For 2P1/2 state, L = 1, S = ½, J = ½ ⇒ g = 2/3
(iii) For 2S1/2 state, L = 0, S = ½, J = ½ ⇒ g = 2
Problem 3. Show that the velocity of the electron in the first orbit of hydrogen atom is (1/137)c, where c is the velocity of light.
Solution: me vrn = nh
Problem 4. How many different types of terms can two electron system consisting of d and f electrons possess?
Solution: For d electrons, we have l1 = 2 and f electrons l2 = 3
All these states are triplet state.
Problem 5. Obtain L.S. in terms of L, S, J. Calculate the possible values of L.S. of L = 1 and S = ½ .
Solution: J = J + S
For the lower level: L = 1, S = 1, J = 1, g = 1
It does not split.
For the upper level: L = 2, S = 1, J = 1, g = 1/2
It splits into three sub levels. Normal Zeeman effect is observed.
(iv) 5I5 → 5He4.
Lower level: L = 5, S = 2, J = 4, g = 19/20
Upper level: L = 6, S = 2, J = 5, g = 19/20
Since the two levels have identical Lande ‘g’ factor.
Normal Zeeman pattern is observed.
Problem 8. For K line for Molydenum (Z = 42) has a wavelength of 0.71 Å. Calculate the wavelength of K line of copper (Z = 29).
Problem 13. Find the ratio of population density between the two states in a He-Ne laser capable of producing light of wavelength 632.8 nm at 300 K.
Problem 14. What is the minimum wavelength of X-rays emitted by an X-ray operating at 50 kV.