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:E_{3} = −13.6Z^{2}/3^{2} and E_{4} = −13.6Z^{2}/4^{2}

ΔE = E_{4} − E_{3}

ΔE = ( −13.6Z^{2}/4^{2})-( −13.6Z^{2}/3^{2})

ΔE = 13.6Z^{2}[1/3^{2} – 1/4^{2}]

ΔE = 13.6Z^{2}[7/9×16]

32.4 = 13.6Z^{2}[7/9×16]

Z^{2} = (32.4 × 9 × 16)/(13.6×7)

Z^{2} = 49

Z = 7