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JEE Main 201911 JanuaryMorning Shift
Exam
JEE Main
Year
2019
Date
11 January
Shift
Morning Shift
Subject
Physics
Chapter
Dual Nature of Matter

JEE Main 2019 · 11 January · Morning Shift · Physics · Dual Nature of Matter

If the deBroglie wavelength of an electron is equal to 10^ - times...

If the deBroglie wavelength of an electron is equal to 10−10^{-} times the wavelength of a photon of frequency 6×1014Hz6 \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′sconstantPlanck's constant=6.63 \times 10^{-34} \mathrm{~J} . \mathrm{s}Massofelectron=9.1×10−31 kg)Mass of electron \left.=9.1 \times 10^{-31} \mathrm{~kg}\right)

Options

  1. A1.1×106 m/s1.1 \times 10^{6} \mathrm{~m} / \mathrm{s}
  2. B1.7×106 m/s1.7 \times 10^{6} \mathrm{~m} / \mathrm{s}
  3. C1.8×106 m/s1.8 \times 10^{6} \mathrm{~m} / \mathrm{s}
  4. D1.45×106 m/s1.45 \times 10^{6} \mathrm{~m} / \mathrm{s}

Correct answer

D. 1.45×106 m/s1.45 \times 10^{6} \mathrm{~m} / \mathrm{s}

Step-by-step solution

de-Broglie wavelength, \lambda=hmv=\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] v=6.63×10−34×6×10149.1×10−31×3×105v=1.45×106 m/s\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 \times10^{6} \mathrm{~m}/ \mathrm{s} \end{array}
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