Question

In which of the following transition, the emitted frequency of the photon is minimum in $H-$atom?

• A. $4^{th}$ orbit to $3^{rd}$ orbit
• B. $5^{th}$ orbit to $4^{th}$ orbit
• C. $3^{rd}$ orbit to $2^{nd}$ orbit
• D. $3^{rd}$ orbit to $1^{st}$ orbit

Answer 1

The correct option is B $5^{th}$ orbit to $4^{th}$ orbit

$\left(A\right)$

$\frac{1}{\lambda }=R_H(\frac{1}{h_1^2}-\frac{1}{h_2^2})$

$\frac{1}{\lambda }=R_H(\frac{1}{3^3}-\frac{1}{4^2})$

$\frac{1}{\lambda }=R_H\times \frac{7}{144}$

$\frac{c}{d}=\frac{7R_{H}C}{144}\Rightarrow \lambda =\frac{7R_{H}C}{144}$

$\left(B\right)$

$\lambda =R_{H}C(\frac{1}{4^2}-\frac{1}{5^2})$

$\frac{9R_{H}C}{400}$

$\left(C\right)$

$\lambda =R_{H}C(\frac{1}{2^2}-\frac{1}{3^3})$

$\lambda =\frac{5R_{H}C}{36}$

$\left(D\right)$

$\lambda =R_{H}C(\frac{1}{1^2}-\frac{1}{3^3})$

$\lambda =\frac{8}{9}{R}_{H}C$

option $B$ has minimum frequency