Question

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

Answer 1

Answer: 4

$n\lambda =2\pi r$

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

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

${\lambda }_2=2\pi \times 0.529\times \frac{2}{Z}$ ------ (ii)

Eq (i) ÷ (ii)

$\frac{{\lambda }_n}{{\lambda }_2}=2=\frac{n}{2}$

$n=4$