Physics - Modern Physics Question with Solution | TestHub

The electron wavelength is given by $\lambda =\frac{h}{mv}$. Velocity $v$ is proportional to $\frac{Z}{n}$, where $Z$ is the atomic number and $n$ is the energy level.

Therefore, $\lambda \propto \frac{n}{Z}$. For hydrogen, $Z=1$.

The ratio of wavelengths is $\frac{{\lambda }_1}{{\lambda }_0}=\frac{n_1}{n_0}=\frac{2^2}{1^2}=4$.

Since $\lambda \propto n$, $\frac{{\lambda }_1}{{\lambda }_0}=\frac{n_1}{n_0}$.

The radius $r\propto n^2$, so the circumference $2\pi r\propto n^2$.

Thus, $\lambda \propto n^2$.

Therefore, $\frac{{\lambda }_1}{{\lambda }_0}=\frac{2^2}{1^2}\times 4=16$.

$P=16$.