Question

If the radius of the first Bohr orbit is r, the wavelength of an electron in the 4th orbit of a hydrogen atom is equal to:

• A. $8\pi r$
• B. $2\pi r$
• C. $6\pi r$
• D. $4r$

Answer 1

The correct option is A $8\pi r$

Angular momentum $m{v}_n{r}_n=\frac{nh}{2\pi }\Rightarrow {\lambda }_n=\frac{h}{m{v}_n}=\frac{2\pi r_n}{n}$,
So, for n = 4, ${\lambda }_4=\frac{2\pi r_4}{4}=\frac{2\pi \left(16r\right)}{4}=8\pi r$