If the deBroglie wavelength of an electron is equal to $10^{-}$ times the wavelength of a photon of…

If the deBroglie wavelength of an electron is equal to $10^{-}$ times the wavelength of a photon of frequency $6 \times 10^{14}$ $\mathrm{Hz}$, then the speed of electron is equal to : (Speed of light $\left.=3 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)$ Planck's constant $=6.63 \times 10^{-34} \mathrm{~J} . \mathrm{s}$ Mass of electron $\left.=9.1 \times 10^{-31} \mathrm{~kg}\right)$
  1. $1.1 \times 10^{6} \mathrm{~m} / \mathrm{s}$
  2. $1.7 \times 10^{6} \mathrm{~m} / \mathrm{s}$
  3. $1.8 \times 10^{6} \mathrm{~m} / \mathrm{s}$
  4. $1.45 \times 10^{6} \mathrm{~m} / \mathrm{s}$

Solution

de-Broglie wavelength, $ \lambda=\frac{\mathrm{h}}{\mathrm{mv}}=10^{-3}\left(\frac{3 \times 10^{8}}{6 \times 10^{14}}\right) \quad\left[\because \lambda=\frac{\mathrm{c}}{\mathrm{v}}\right] $ $ \begin{array}{l} \mathrm{v}=\frac{6.63 \times 10^{-34} \times 6 \times 10^{14}}{9.1 \times 10^{-31} \times 3 \times 10^{5}} \\ \mathrm{v}=1.45 \times 10^{6} \mathrm{~m} / \mathrm{s} \end{array} $

Asked in: JEE Main 2019 (11 Jan Shift 1)

Practice more Dual Nature of Matter questions on Aicharya