What will be the speed of an electron if it's de Broglie wavelength is equal to 10−3 times the wavelength of a photon of frequency 6×1014Hz? (Speed of light 3×108m/s; Planck's constant =6.63×10−34J.s; Mass of electron =9.1×10−31kg

For photon v=cλλp=Cv=3×1086×1014=12×10−6mFor electronλe=10−3×λp=10−92mλ=hp,p=mvV=hλm=6.63×10−3412×10−9×9.1×10−31=1.45×106

What will be the speed of an electron if it's de Broglie wavelength is equal to 10−3 times the wavelength of a photon of frequency 6×1014Hz? (Speed of light 3×108m/s; Planck's constant =6.63×10−34J.s; Mass of electron =9.1×10−31kg

For photon v=cλλp=Cv=3×1086×1014=12×10−6mFor electronλe=10−3×λp=10−92mλ=hp,p=mvV=hλm=6.63×10−3412×10−9×9.1×10−31=1.45×106

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What will be the speed of an electron if it's de Broglie wavelength is equal to $10^{- 3}$ times the wavelength of a photon of frequency $6 \times 10^{14} Hz ?$
(Speed of light $3 \times 10^{8} m / s$ ; Planck's constant $= 6.63 \times 10^{- 34} J . s;$ Mass of electron $= 9.1 \times 10^{- 31} kg)$

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$1.7 \times 10^{6} m / s$

$1.45 \times 10^{6} m / s$

$1.8 \times 10^{6} m / s$

$1.1 \times 10^{6} m / s$

answer is B.

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Detailed Solution

For photon $v = \frac{c}{λ}$

$λ_{p} = \frac{C}{v} = \frac{3 \times 10^{8}}{6 \times 10^{14}} = \frac{1}{2} \times 10^{- 6} m$

For electron

$\begin{array}{l} λ_{e} = 10^{- 3} \times λ_{p} = \frac{10^{- 9}}{2} m \\ λ = \frac{h}{p}, p = mv \\ V = \frac{h}{λ m} = \frac{6.63 \times 10^{- 34}}{\frac{1}{2} \times 10^{- 9} \times 9.1 \times 10^{- 31}} = 1.45 \times 10^{6} \end{array}$

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What will be the speed of an electron if it's de Broglie wavelength is equal to 10−3 times the wavelength of a photon of frequency 6×1014Hz? (Speed of light 3×108m/s; Planck's constant =6.63×10−34J.s; Mass of electron =9.1×10−31kg

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What will be the speed of an electron if it's de Broglie wavelength is equal to $10^{- 3}$ times the wavelength of a photon of frequency $6 \times 10^{14} Hz ?$
(Speed of light $3 \times 10^{8} m / s$ ; Planck's constant $= 6.63 \times 10^{- 34} J . s;$ Mass of electron $= 9.1 \times 10^{- 31} kg)$