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. $4\pi a_{0}$
• B. $8\pi a_{0}$
• C. $6\pi a_{0}$
• D. $2\pi a_{0}$

Answer 1

Answer: (C)

$r_{3} = a_{0}n^{2}$
$r = a_{0} \times \left(3\right)^{2} = 9a_{0}$
$mvr = \frac{nh}{2\pi};$
$mv = \frac{nh}{2\pi r} = \frac{3h}{2\pi r\times9a_{0}} = \frac{h}{6\pi\,a_{0}}$
$\lambda = \frac{h}{mv} = \frac{h}{h} \times 6\pi a_{0} = 6\pi a_{0}$