Question

If the radius of first Bohr's orbit of hydrogen atom is 'x' then de Broglie wavelength of electron in
3rd orbit is nearly
(A) 2πx
(B) 6πx
(C) 9x
(D) x/3​

Answer 1

Broglie wavelength of the electron in  the 3rd orbit would nearly be the 6πx.

Explanation:

Given,

$r_{1}$ = x

As per Bohr's postulate,

$mv_{n} r_{n}$ = nh/2π (nth orbit)

As we know that,

Radius in nth orbit equals to $r_{n} = n^{2} .r_{1}$

A.T.Q.

In 3rd orbit = m.$v_{3} r_{3}$ = 3h/2π

To find Broglie wavelength of electron, we will use;

λ = h/$m_{3} v_{3}$

so,

λ = (2π.$r_{3}$)/3

λ = [2π $(3)^2$x]/3

∵ λ = 6πx

Thus, the Broglie wavelength of the electron in  3rd orbit would be likely 6πx.

Learn more: Wavelength

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