Question

The de-Broglie wavelength of an electron in the first Bohr orbit is

• A. Equal to one fourth the circumference of the first orbit
• B. Equal to twice the circumference of the first orbit
• C. Equal to half the circumference of the first orbit
• D. Equal to the circumference of the first orbit

Answer 1

The correct option is D Equal to the circumference of the first orbit

$mv{r}_n=\frac{nh}{2\pi }$

$\Rightarrow p{r}_n=\frac{nh}{2\pi }$

$\Rightarrow \frac{h}{\lambda }\times r_n=\frac{nh}{2\pi }$

$\Rightarrow \lambda =\frac{2\pi r_n}{n}$, for first orbit $n=1$ so $\lambda =2\pi r_1$
= circumference of first orbit