JEE MAIN - Chemistry (2022 - 26th July Morning Shift - No. 17)
The wavelength of an electron and a neutron will become equal when the velocity of the electron is $$x$$ times the velocity of neutron. The value of $$x$$ is ____________. (Nearest Integer)
(Mass of electron is $$9.1 \times 10^{-31} \mathrm{~kg}$$ and mass of neutron is $$1.6 \times 10^{-27} \mathrm{~kg}$$ )
Answer
1758
Explanation
$$\lambda_{e}=\frac{h}{m_{e} \times V_{e}}, \quad \lambda_{N}=\frac{h}{m_{N} \times V_{N}}$$
$$\lambda_{e}=\lambda_{N}$$ When $$V_{e}=x V_{N}$$
$$\frac{1}{m_{e} V_{e}}=\frac{1}{m_{N} \times V_{N}}$$
$$\frac{m_{N}}{m_{e}}=\frac{V_{e}}{V_{N}}=x$$
$$x=\frac{1.6 \times 10^{-27}}{9.1 \times 10^{-31}}$$
$$=0.17582 \times 10^{4}$$
$$\simeq 1758$$
$$\lambda_{e}=\lambda_{N}$$ When $$V_{e}=x V_{N}$$
$$\frac{1}{m_{e} V_{e}}=\frac{1}{m_{N} \times V_{N}}$$
$$\frac{m_{N}}{m_{e}}=\frac{V_{e}}{V_{N}}=x$$
$$x=\frac{1.6 \times 10^{-27}}{9.1 \times 10^{-31}}$$
$$=0.17582 \times 10^{4}$$
$$\simeq 1758$$
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