Question

When an electron makes transition from $\left(n+1\right)$ state to n state the wavelength of emitted radiations is related to $n(n>>>1)$according to $\lambda \propto n^x$. What is the value of $x$ ?

Answer 1

Answer: 3

$\frac{1}{\lambda }=R{Z}^2\left(\frac{1}{n^2}-\frac{1}{{\left(n+1\right)}^2}\right)$
$\frac{1}{\lambda }=R{Z}^2\frac{{\left(n+1\right)}^2-n^2}{n^2{\left(n+1\right)}^2}$
$\frac{1}{\lambda }=R{Z}^2\frac{\left(n+1+n\right)\left(n+1-n\right)}{n^2\left(n+1\right)}$
$\frac{1}{\lambda }=R{Z}^2\frac{\left(2n+1\right)}{n^2{\left(n+1\right)}^2}$
$\lambda \propto n^3$
$x=3$