If $\mathrm{a}_{0}$ is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength ($\lambda$) of the electron present in the second orbit of hydrogen atom? [n: any integer]

JEE Main · 2025 · 29 Jan 2025 · Shift 1 · Atomic Structure

a_{0}

is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength (

λ

) of the electron present in the second orbit of hydrogen atom? [n: any integer]

Answer: (B)

Bohr's quantisation postulate requires the circumference of an orbit to hold a whole number of de Broglie wavelengths,

2 π r = nλ

. In the second orbit of the hydrogen atom the radius is

r_{2} = 2^{2} a_{0} = 4 a_{0}

. Substituting,

2 π (4 a_{0}) = nλ ⟹ λ = \frac{8 π a _{0}}{n}

JEE Main · 2025 · 29 Jan 2025 · Shift 1 · Single correct option