Question

In hydrogen atom,the de Broglie wavelength of an electron in the second Bohr's orbit is ? Given that Bohr radius $a_0=52.9pm$

• A. $211.6pm$
• B. $211.6\pi pm$
• C. $52.9\pi pm$
• D. $105.8pm$

Answer 1

The correct option is C $52.9\pi pm$

Since,
$mvr=\frac{nh}{2\pi }p\times r=\frac{nh}{2\pi }p=\frac{2\times h}{2\times \pi \times 52.9}=\frac{h}{52.9\pi }$
Also,
$\lambda =\frac{h}{p}$
Putting the value of $p$
$\lambda =\frac{h}{\frac{h}{52.9\pi }}=52.9\pi pm$