Question

Ratio of difference in energy between the energy levels with $n=3$ and $n=4$ and between the energy levels with $n=8$ and $n=9$ for a hydrogen like atom or ion is

• A. $0.71$
• B. $0.41$
• C. $2.43$
• D. $14.82$

Answer 1

The correct option is D $14.82$

Energy difference between $n=3$ and $n=4$
$E_1=K[\frac{1}{3^2}-\frac{1}{4^2}]$

Energy difference between $n=8$ and $n=9$
$E_2=K[\frac{1}{8^2}-\frac{1}{9^2}]$

Ratio of energy difference :
Energy $=\frac{E_1}{E_2}=\frac{\frac{1}{9}-\frac{1}{16}}{\frac{1}{64}-\frac{1}{81}}=\frac{7\times 64\times 81}{9\times 15\times 17}$$=$ $14.8235$