Question

A hydrogen-like atom emits radiations of frequency $2.7\times {10}^{15}Hz$ when it makes a transition from $n=2$ to $n=1$. The frequency emitted in a transition from $n=3$ to $n=1$ will be

• A. $1.8\times {10}^{15}Hz$
• B. $3.2\times {10}^{15}Hz$
• C. $4.7\times {10}^{5}Hz$
• D. $6.8\times {10}^{15}Hz$

Answer 1

The correct option is B $3.2\times {10}^{15}Hz$

${\nu }_{2\to 1}=\frac{13.6\times Z^2}{h}(\frac{1}{1}-\frac{1}{4})=\frac{3}{4}\times \frac{13.6\times Z^2}{h}Hz$ $=2.7\times {10}^{15}Hz$

Now, for transition from $n=3$ to $n=1$: ${\nu }_{3\to 1}=\frac{13.6\times Z^2}{h}(\frac{1}{1}-\frac{1}{9})$

$=\frac{8}{9}\times \frac{13.6\times Z^2}{h}Hz$

$=\frac{8}{9}\times \frac{4}{3}\times 2.7\times {10}^{15}Hz$

$=3.2\times {10}^{15}Hz$