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

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If the radius of first Bohr's orbit is

x

, then de Broglie wavelength of an electron in

3^{rd}

orbit is nearly

PhysicsAtomic PhysicsJEE Main

Options:

A $2πx$
B $6πx$
C $9x$
D $x/3$

Solution:

2634 Upvotes Verified Answer

The correct answer is:

6πx

If $r_{3} =$ Radius of $3^{rd}$ orbit

and $r_{1} =$ Radius of $1^{st}$ orbit

$r_{3} = r_{1} \times n^{2} = x \times 3^{2} = 9x$

$∵ 2 {πr}_{3} = nλ$

$∴ λ = \frac{2 {πr}_{3}}{n} = \frac{2 π \times 9 x}{3} = 6 πx$

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