If a0 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 ]

de Broglie Wavelength of Electron in Second Orbit | JEE Mains PYQ | Structure of Atom

Q. If a₀ 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 ]

(A) 8πa₀ / n

(B) 2a₀ / nπ

(D) 4πa₀ / n

Explanation

Step 1: Bohr’s quantization condition

According to Bohr model:
2πr_n = nλ

Step 2: Radius of nth orbit

For hydrogen atom:
r_n = n²a₀

Step 3: Substitute r_n in Bohr condition

2π(n²a₀) = nλ
λ = 2πn a₀

Step 4: Write in general form

λ = 8πa₀ / n

Correct Answer = 8πa₀ / n (Option A)

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