First slide

Hydrogen -like ion

Question

If de Broglie wavelength of electron in the ground state of hydrogen atom is $λ$ , what will be the de Broglie wavelength of the electron in $H e^{+}$ when the ion is in the second excited state?

Moderate

A

$λ$
B

3 $λ$
C

1.5 $λ$
D

2 $λ$

Solution

If $r_{0}$ be the radius of orbit of electron in hydrogen atom in ground state, then de Broglie wavelength $λ = 2 π r_{0}$
In a hydrogen-like ion, $r_{n} = r_{0} \frac{n^{2}}{z}$
$∴$ de Broglie wavelength of electron
$λ^{1} = \frac{2 π r_{n}}{n} = 2 π r_{0} \frac{n}{z} = λ \frac{3}{2} = 1.5 λ$

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