If the radius of the first orbit of hydrogen atom is a₀, then de Broglie's wavelength of electron in 3rd orbit is:

De Broglie Wavelength of Electron in 3rd Orbit | JEE Main PYQ | Structure of Atom

Q. If the radius of the first orbit of hydrogen atom is a₀, then de Broglie's wavelength of electron in 3rd orbit is:

(A) πa₀³ / 6

(B) 3πa₀

(D) πa₀³ / 3

Correct Answer: 6πa₀

Explanation

According to Bohr–de Broglie condition:

2πrₙ = nλ

⇒ λ = 2πrₙ / n

Radius of nth orbit:

rₙ = n²a₀

For 3rd orbit (n = 3):

r₃ = 3²a₀ = 9a₀

λ = (2π × 9a₀) / 3

λ = 6πa₀

Hence, de Broglie wavelength of electron in 3rd orbit is 6πa₀.

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