Chemistry - Atomic Structure Question with Solution | TestHub

According to De-Broglie's wavelength,

$n\lambda =2\pi r$

Substituting $r=a_0\frac{n^2}{Z}$, we get:

$n\lambda =2\pi a_0\frac{n^2}{Z}$

$\lambda =2\pi a_0\left(\frac{n}{Z}\right)$

For the first case, let's assume $n=4$ and $Z=4$:

${\lambda }_1=2\pi a_0\left(\frac{4}{4}\right)=2\pi a_0$

For the second case, let's assume $n=8$ and $Z=2$:

${\lambda }_2=2\pi a_0\left(\frac{8}{2}\right)=8\pi a_0$

Therefore, the ratio of the wavelengths is:

$\frac{{\lambda }_2}{{\lambda }_1}=\frac{8\pi a_0}{2\pi a_0}=4$