If the radius of first orbit of H atom is a0, the de- Broglie wavelength of an electron in the third orbit is

Question

If the radius of first orbit of H atom is a0, the de- Broglie wavelength of an electron in the third orbit is (A) 4π a0 (B) 8π a0 (C) 6π a0 (D) 2π a0

Tardigrade Admin · Accepted Answer

r3 = a0n2 r = a0 × (3)2 = 9a0 mvr = (nh/2π); mv = (nh/2π r) = (3h/2π r×9a0) = (h/6π a0) λ = (h/mv) = (h/h) × 6π a0 = 6π a0

Q. If the radius of first orbit of H atom is $a_{0}$ , the de- Broglie wavelength of an electron in the third orbit is