Question

Calculate the wavelength of an electron moving with velocity 90% of the speed of the light

Answer 1

Answer:

See the attachment.......

Answer 2

Answer:

The de Broglie wavelength of an electron moving with velocity v = 9c/10 is $0.26*10^{-10}m$

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 $90$ % of light velocity

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

⇒ velocity $v=C*90/100=9C/10m/s$

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

put all the values in equation 1

⇒λ= $\frac{6.6*10^{-34} }{9.1*10^{-31}*9C/10}=0.26*10^{-10} m$