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

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If the radius of first Bohr's orbit of hydrogen is

x

, then de-Broglie wavelength of electron in its 3rd orbit is

ChemistryStructure of AtomJEE Main

Options:

A $2 π x$
B $6 π x$
C $9 x$
D $\frac{x}{3}$

Solution:

1814 Upvotes Verified Answer

The correct answer is:

6 π x

r_{n} \propto \frac{n^{2}}{z}

for Hydrogen atom,

r_{n} \propto n^{2}

r_{1} = x

r_{3} = 9 x

Now,

\Rightarrow {2πr}_{3} = nλ

\Rightarrow λ= \frac{2 {πr}_{3}}{3}

\Rightarrow λ= \frac{2}{3} π \times 9x

∴ λ = 6 πx

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