Question

Calculate the number of waves made by a Bohr electron in one complete revolution in nth orbit of $He^{+}$ ion, if ratio of de-Broglie wavelength associated with electron moving in n^th orbit and 2^nd orbit is $2.0$ :-

Answer 1

$n\lambda =2\pi r$

$n\lambda =2\times \pi \times 0.529\times \frac{n^{2}}{Z}$

$\lambda _{n}=2\pi \times 0.529\times \frac{n}{Z}$ ------ (i)

$\lambda _{2}=2\pi \times 0.529\times \frac{2}{Z}$ ------ (ii)

Eq (i) ÷ (ii)

$\frac{\lambda _{n}}{\lambda _{2}}=2=\frac{n}{2}$

$n=4$