Question

An electron is moving with the velocity equal to 10percent of the velocity of light. Its debroglie wavelength will be

Answer 1

Velocity of light = 3 ×108m/s

10% of velocity of light = 10100×3×108 m/s=0.3 ×108m/s

h = Planck's constant = 6.63 × 10-34Js

​m = mass of electron = 9.1 × 10-31Kg

  λ= hmv         λ =6.63×10−34Js9.1 ×10−31kg×0.3×108ms−1   = 2.42 × 10−11 m

  = 24.2pm   

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Answer 2

Answer:

The de Broglie wavelength of an electron moving with velocity v = c/10 is $0.24*10^{-10}m$

Explanation:

• The de Broglie wavelength is the wavelength of matter in wave nature

• For a particle with mass (m) and moving with velocity (v), the de Broglie wavelength is given by the formula

       λ =$h/p=h/mv$    (equation 1)

      where Planck's constant $h=6.6*10^{-34}$

     $p$- the momentum of the particle

From the question, the given particle is an electron

the velocity of the electron is $10$ % of light velocity

where the velocity of light $C=3*10^{8}m/s$

⇒ velocity $v=C*10/100=C/10=3*10^{7}m/s$

mass of the electron $m=9.1*10^{-31}kg$

put all the values in equation 1

⇒λ= $\frac{6.6*10^{-34} }{9.1*10^{-31}*3*10^{7} }=0.24*10^{-10} m$