Question

For a hydrogenic ion kinetic energy of electron in its 3^rd excited state is found to be 54.4 eV. Then series limit $\left( \frac{1}{\lambda} \right)$ for Balmer series, for this ion, is –

• A. 109678 × 16 cm^–1
• B. 109678/16 cm^–1
• C. 109678 × 4 cm^–1
• D. 109678 × 64 cm^–1

Answer 1

Answer: (A)

109678 × 16 cm^–1

Answer 2

K.E = 13.6 $\frac{Z^{2}}{n^{2}}$ ev/atom Ž 54.4 = 13.6 × $\frac{Z^{2}}{4^{2}}$

Ž Z² = 64

for Balmer series –

$\frac{1}{\lambda}$ = RZ² $\left\lbrack \frac{1}{2^{2}}–\frac{1}{\infty^{2}} \right\rbrack$ (for series limit)

= 109678 × 64 $\left\lbrack \frac{1}{4}–\frac{1}{\infty} \right\rbrack$ cm^–1

= 109678 × 16 cm^–1