devarshi-dt-logo

Question:

If the de Broglie wavelength of the electron in nth Bohr orbit in a hydrogenic atom is equal to 1.5πa₀ (a₀ is Bohr radius), then the value of n/z is:

1.0

0.75

0.40

1.50

Solution:

According to de-Broglie's hypothesis
2πr = nλ ⇒ 2π × a₀ = nλ
Given that λ = 1.5πa₀
Substituting this value in the above equation,
2πa₀ = n(1.5πa₀)
2πa₀ = 1.5nπa₀
n = 2/1.5 = 4/3
For hydrogenic atom, r = a₀n²/z
2π(a₀n²/z) = nλ
2π(a₀n²/z) = n(1.5πa₀)
2n/z = 1.5
n/z = 1.5/2 = 0.75
So, the correct option is B