Question

If the radius of first orbit of H - atom is $a_0$, then de Broglie wavelength of electron in 4th orbit is ?

• A. $2\pi a_0$
• B. $16a_0$
• C. $\frac{a_0}{4}$
• D. $8\pi a_0$

Answer 1

The correct option is D

$8\pi a_0$

$r_n=a_0\times n^2,r_4=a_0\times 4^2=16a_{0}mv=4.\frac{h}{2\pi r_4}=\frac{4h}{2\pi \times 16a_0}=\frac{h}{8\pi a_0}\lambda =\frac{h}{mv}=8\pi a_0$