Question

The radius of the orbit of an electron in a Hydrogen-like atom is $3a_0$, where $a_0$ is the Bohr radius. Its orbital angular momentum is $\frac{3h}{2\pi }$. It is given that h is Planck's constant and R is Rydberg constant. The possible wavelength, when the atom de-excites is :

• A. $\frac{4}{5R}$
• B. $\frac{4}{9R}$
• C. $\frac{1}{2R}$
• D. $\frac{9}{32R}$

Answer 1

The correct option is D $\frac{9}{32R}$

solution:

given ;

$4.5a_0=a_0\frac{n^2}{Z}----\left(i\right)$

$\frac{nh}{2\pi }=\frac{3h}{2\pi }----\left(ii\right)$

so , n= 3 and z=2

so , possible wavelength are:

$\frac{1}{{\lambda }_1}=R{Z}^2[\frac{1}{1^2}-\frac{1}{3^2}]\Rightarrow {\lambda }_1=\frac{9}{32R}$

hence the correct option:D