Verified Solution • 2025–26 Session moderate

QJEEM23Ch591b: JEE Main 2023 Chemistry - Class 11 JEEM23Ch591b Solution: The wavelength of an electron of kinetic energy J is _________…

The wavelength of an electron of kinetic energy 4.50×10−294.50\times10^{-29} J is _________ ×10−5\times 10^{-5} m. (Nearest integer)

Given : mass of electron is 9×10−319\times10^{-31} kg, h =6.6×10−34=6.6\times10^{-34} J s

Step-by-Step Verified Solution

amp;λd=hmv=h2mKE=6.6×10−342×9×10−31×4.5×10−29amp;=6.6×10−3492×10−60amp;=6.6×10−349×10−30=6.69×10−4amp;=7.3×10−5 m\begin{aligned}& \lambda_{\mathrm{d}}=\frac{\mathrm{h}}{\mathrm{mv}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mKE}}}=\frac{6.6 \times 10^{-34}}{\sqrt{2 \times 9 \times 10^{-31} \times 4.5 \times 10^{-29}}} \\\\& =\frac{6.6 \times 10^{-34}}{\sqrt{9^2 \times 10^{-60}}} \\\\& =\frac{6.6 \times 10^{-34}}{9 \times 10^{-30}}=\frac{6.6}{9} \times 10^{-4} \\\\& =7.3 \times 10^{-5} \mathrm{~m}\end{aligned}

Therefore Ans =7=7

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