de-Broglie wavelength of an electron orbiting in the state of hydrogen atom is close to (Given Bohr radius = 0.052 nm) [2025]

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Solution

Q.
de-Broglie wavelength of an electron orbiting in the $n = 2$ state of hydrogen atom is close to (Given Bohr radius = 0.052 nm) [2025]

1 1.67 nm

2 2.67 nm

3 0.067 nm

4 0.67 nm

Ans.
(4)

$2 π r = n λ \Rightarrow λ = \frac{2 π r}{n} = \frac{2 π \times (0.052) \frac{n^{2}}{Z}}{n}$

$∴$ $λ = 2 π \times (0.052) \times 2 \approx 0.67 nm$

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