Question

In the hydrogen atom spectrum ${\lambda }_{3-1}and{\lambda }_{2-1}$ represent wavelengths emitted due to transition from second and first excited states to the ground state respectively. The value of $\frac{{\lambda }_{3-1}}{{\lambda }_{2-1}}$ is :

• A. $27/32$
• B. $32/27$
• C. $4/9$
• D. $9/4$

Answer 1

Answer: (A)

$27/32$

$\frac{1}{{\lambda }_{3-1}}=R\left(\begin{array}{c}\frac{1}{1^2}-\frac{1}{3^2}\end{array}\right)=\frac{8R}{9}$
$\frac{1}{{\lambda }_{2-1}}=R\left(\begin{array}{c}\frac{1}{1^2}-\frac{1}{2^2}\end{array}\right)=\frac{3R}{4}$
$\Rightarrow \frac{{\lambda }_{3-1}}{{\lambda }_{2-1}}=\frac{27}{32}$