Verified Solution • 2025–26 Session moderate

QJEEM22Ch8ba8: JEE Main 2022 Chemistry - Class 11 JEEM22Ch8ba8 Solution: The wavelength of an electron and a neutron will become equal…

The wavelength of an electron and a neutron will become equal when the velocity of the electron is xx times the velocity of neutron. The value of xx is ____________. (Nearest Integer)

(Mass of electron is 9.1×10−31 kg9.1 \times 10^{-31} \mathrm{~kg} and mass of neutron is 1.6×10−27 kg1.6 \times 10^{-27} \mathrm{~kg} )

Step-by-Step Verified Solution

λe=hme×Ve,λN=hmN×VN\lambda_{e}=\frac{h}{m_{e} \times V_{e}}, \quad \lambda_{N}=\frac{h}{m_{N} \times V_{N}}

λe=λN\lambda_{e}=\lambda_{N} When Ve=xVNV_{e}=x V_{N}

1meVe=1mN×VN\frac{1}{m_{e} V_{e}}=\frac{1}{m_{N} \times V_{N}}

mNme=VeVN=x\frac{m_{N}}{m_{e}}=\frac{V_{e}}{V_{N}}=x

x=1.6×10−279.1×10−31x=\frac{1.6 \times 10^{-27}}{9.1 \times 10^{-31}}

=0.17582×104=0.17582 \times 10^{4}

≃1758\simeq 1758

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