JEE MAIN - Chemistry (2024 - 6th April Morning Shift - No. 30)
Frequency of the de-Broglie wave of electron in Bohr's first orbit of hydrogen atom is _________ $$\times 10^{13} \mathrm{~Hz}$$ (nearest integer).
[Given : $$\mathrm{R}_{\mathrm{H}}$$ (Rydberg constant) $$=2.18 \times 10^{-18} \mathrm{~J}, h$$ (Plank's constant) $$=6.6 \times 10^{-34} \mathrm{~J} . \mathrm{s}$$.]
Explanation
$$\begin{aligned} & \lambda=\frac{h}{m v} \\ & \lambda \cdot v=\frac{h}{m} \\ & \frac{\lambda \cdot v^2}{v}=\frac{h}{m} \\ & \frac{v^2}{\text { Frequency }}=\frac{h}{m} \end{aligned}$$
$$\begin{aligned} & \text { Frequency }=\frac{\mathrm{mv}^2}{\mathrm{~h}}=\frac{2 \mathrm{R}_{\mathrm{H}}}{\mathrm{h}} \\ & =\frac{2 \times 2.18 \times 10^{-18}}{6.6 \times 10^{-34}} \\ & =660.6 \times 10^{13} \mathrm{~Hz} \end{aligned}$$
Nearest integer $$=661$$
If we take $$h=6.626 \times 10^{-34}$$
Then
$$\begin{aligned} \text { Frequency } & =\frac{2 R_H}{h} \\ & =658.01 \times 10^{13} \mathrm{~Hz} \end{aligned}$$
But if value of $$\mathrm{h}$$ is given as $$6.6 \times 10^{-34}$$ correct answer will be 661.
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