Q. An electron revolves round a nucleus of atomic number Z. If 32.4 eV of energy is required to excite an electron from the n = 3 state to n = 4 state, then the value of Z is
(a) 5
(b) 6
(c)4
(d) 7
Ans: (d)
Sol:E3 = −13.6Z2/32 and E4 = −13.6Z2/42
ΔE = E4 − E3
ΔE = ( −13.6Z2/42)-( −13.6Z2/32)
ΔE = 13.6Z2[1/32 – 1/42]
ΔE = 13.6Z2[7/9×16]
32.4 = 13.6Z2[7/9×16]
Z2 = (32.4 × 9 × 16)/(13.6×7)
Z2 = 49
Z = 7