Question

The kinetic energy of a particle is equal to the energy of a photon. The particle moves at 6.1% of the speed of light. Find the ratio of the photon wavelength to the de Broglie wavelength of the particle. Take the speed to be non-relativistic.

Answer 1

Kinetic energy K = energy of photon

( 1/ 2) m v ² = hc /

Where v = speed of the particle

             = 6.1 % of c

            = ( 6.1 / 100 ) x c

           = 0.061 c

( 1/ 2) m (0.061 c ) ² = hc /

1.8605 x 10 ^-3 mc ² = hc /

1.8605 x 10 ^-3 mc= h /

Photon wavelength = h / [1.8605 x 10 ^-3 mc]

de Broglie wavelength of the particle = h / mv

the ratio of the photon wavelength to the de Broglie wavelength of the particle

    / = { h / [1.8605 x 10 ^-3 mc] } / { h / mv }

             = mv / [1.8605 x 10 ^-3 mc]

            = v / [1.8605 x 10 ^-3 c]

           = 0.061 c / [1.8605 x 10 ^-3 c]

           = 0.061 / [1.8605 x 10 ^-3 ]

           = 32.78