Frequency of the de-Broglie wave of election in Bohr's first orbi… - Vidyadip

MCQ

Frequency of the de-Broglie wave of election in Bohr's first orbit of hydrogen atom is. . . . . . . . . . $\times 10^{13} \mathrm{~Hz}$ (nearest integer).

[Given : $R_{\mathrm{H}}\left(\right.$ Rydberg constant) $=2.18 \times 10^{-18} \mathrm{~J}$.

$h($ Plank's constant $)=6.6 \times 10^{-34}$ J.s. $]$

A
$600$
B
$657$
✓
$658$
D
$660$

✓

Answer

Correct option: C.

$658$

c
$\lambda=\frac{\mathrm{h}}{\mathrm{mv}}$

$\lambda=\frac{\mathrm{hv}}{\mathrm{mv}^2}$

$\frac{\mathrm{mv}^2}{\mathrm{~h}}=\frac{\mathrm{v}}{\lambda}=\mathrm{v} \text { (frequency) }$

$\text { Given } \frac{1}{2} \mathrm{mv}^2=2.18 \times 10^{-18} \mathrm{~J}$

$\mathrm{~h}=6.6 \times 10^{-34}$

$\mathrm{v}=\frac{4.36 \times 10^{-18}}{6.6 \times 10^{-34}}=660.60 \times 10^{13} \mathrm{~Hz}$

$\approx 661 \times 10^{13} \mathrm{~Hz}$

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