First slide

Matter waves (DC Broglie waves)

Question

If de broglie wavelength of electron in the ground state of hydrogen atom is $λ,$ what is the de Broglie wavelength of electron in the first excited state of $H e^{+} i o n ?$

Moderate

A

$2 λ$
B

$\frac{λ}{2}$
C

$λ$
D

$\frac{λ}{4}$

Solution

(3)
For a hydrogen - like ion, speed of electron $V = V_{0} . \frac{Z}{n} w h e r e V_{0}$ is the speed of electron in the ground state of H - atom.
$∴ d e b r o g l i e w a v e l e n g t h = \frac{h}{m v} = \frac{h}{m V_{0}} . (\frac{n}{z})$
$\begin{array}{l} ∴ λ = \frac{h}{m v_{0}} (\frac{1}{1}) a n d λ^{'} = \frac{h}{m V_{0}} . (\frac{2}{2}) = \frac{h}{m V_{0}} \\ ∴ λ^{'} = λ \end{array}$

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