Question

The de-Broglie wavelength of an electron in $4^{th}$ orbit is ________. ($r=$ radius of $1^{st}$ orbit)

• A. $2\pi r$
• B. $4\pi r$
• C. $8\pi r$
• D. $16\pi r$

Answer 1

The correct option is C $8\pi r$

According to Bohr's postulates, radii of the $n^{th}$ and the first orbits are related by:

$r_n=n^2{r}_{1}n{\lambda }_n=2\pi r_n\Rightarrow {\lambda }_n=2n\pi r_1$.

Now, for $n=4$, we have:

${\lambda }_4=8\pi r_1=8\pi r$