Question

If the radius of first Bohr's orbit of hydrogen is $\text{x}$ , then the de-Broglie wavelength of the electron in its $3^{rd}$ orbit is

• A. $2\pi x$
• B. $6\pi x$
• C. $9x$
• D. $\frac{x}{3}$

Answer 1

Answer: (B)

$\text{r}_{\text{n}} \propto \frac{\text{n}^{\text{2}}}{\text{z}}$
for Hydrogen atom, (z=1), $\text{r}_{\text{n}} \propto \text{n}^{\text{2}}$
$\text{r}_{\text{1}} = \text{x}$
$\text{r}_{\text{3}} = 9 \text{x}$
Now, $\Rightarrow \text{2\pi r}_{\text{3}} = \text{n\lambda }$
$\Rightarrow \text{\lambda =} \frac{2 \text{\pi r}_{\text{3}}}{3}$
$\Rightarrow \text{\lambda =} \frac{2}{3} \text{\pi } \times \text{9x}$
$\therefore \, \text{\lambda } = 6 \text{\pi x}$