**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 ^{2}P_{3/2} state, L = 1, S = ½, J = 3/2 ⇒ g = 4/3

(ii) For ^{2}P_{1/2} state, L = 1, S = ½, J = ½ ⇒ g = 2/3

(iii) For ^{2}S_{1/2} 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:** m_{e} v_{rn} = 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 l_{1} = 2 and f electrons l_{2} = 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) ^{5}I_{5} → ^{5}He_{4}.

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.*

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