Q44 / 99 · NTA Abhyas (JEE Main) 2020 · Chemistry · Structure of Atom

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

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

Solution

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

Hence, the correct answer is option: 'B'.

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