If the radius of the first orbit of hydrogen atom is , then de Broglie's wavelength of electron in 3rd orbit is [2023]

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Solution

Q.
If the radius of the first orbit of hydrogen atom is $a_{0}$ , then de Broglie's wavelength of electron in 3rd orbit is [2023]

1 $\frac{π a_{0}}{3}$

2 $\frac{π a_{0}}{6}$

3 $3 π a_{0}$

4 $6 π a_{0}$

Ans.
(4)

$r_{n} = a_{0} \times n^{2}, for 3rd orbit r_{3} = 9 a_{0}$

$m V = \frac{3 h}{2 π r_{3}} = \frac{3 h}{2 π 9 a_{0}} = \frac{h}{6 π a_{0}}$

and $λ = \frac{h}{m V} = \frac{h}{\frac{h}{6 π a_{0}}} = 6 π a_{0}$

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