Question

If the radius of first orbit of $H-$atom is $a_0$, the de-Broglie wavelength of an electron in the third orbit is:

• A. $6\pi a_0$
• B. $8\pi a_0$
• C. $2\pi a_0$
• D. $4\pi a_0$

Answer 1

Answer: (A)

$6\pi a_0$

$\lambda =\frac{h}{mV}$

$mVr=\frac{nh}{2\pi }\Rightarrow \frac{h}{mV}$

$\lambda =\frac{2\pi r}{n}$

$r=a_o\times \frac{n^2}{1}$ for H- atoms.

$\therefore \lambda =2\pi a_o\times n$

For $3rd$ orbit $n=3$

$\therefore \lambda =6\pi a_o$