Dual Nature of Matter

JEE Main level, single correct, medium

75 of 200

Question 75 of 200

If the deBroglie wavelength of an electron is equal to 10−10^{-} times the wavelength of a photon of frequency 6×10146 \times 10^{14} Hz\mathrm{Hz}, then the speed of electron is equal to :

(Speed of light =3×108 m/s)\left.=3 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)

Planck's constant =6.63×10−34 J.s=6.63 \times 10^{-34} \mathrm{~J} . \mathrm{s}

Mass of electron =9.1×10−31 kg)\left.=9.1 \times 10^{-31} \mathrm{~kg}\right)

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

de-Broglie wavelength,

λ=hmv=10−3(3×1086×1014)[∵λ=cv]\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]

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 \times 10^{6} \mathrm{~m} / \mathrm{s} \end{array}

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