If the radius of first Bohr's orbit of hydrogen is x , then the de-Broglie wavelength of the electron in its 3 rd orbit is

Question

If the radius of first Bohr's orbit of hydrogen is x , then the de-Broglie wavelength of the electron in its 3 rd orbit is, 2 π x, 6 π x, 9 x, x 3

MARKS App · Accepted Answer

r n ∝ n 2 z for Hydrogen atom, (z=1), r n ∝ n 2 r 1 = x r 3 = 9 x Now, ⇒ 2πr 3 = nλ ⇒ λ= 2 πr 3 3 ⇒ λ= 2 3 π × 9x ∴ λ = 6 πx