First slide

Wave nature of matter

Question

The de-Broglie wavelength of an electron moving with a velocity 1.5 x 10⁸ ms^-1 is equal to that of a photon. The ratio of the kinetic energy of the electron to that of the photon is ________.

Moderate

Solution

$We use \frac{h}{m v} = λ \Rightarrow \frac{E_{k}}{E_{p h}} = \frac{\frac{1}{2} m v^{2}}{\frac{h c}{λ}} = \frac{m^{2} v^{2} λ}{2 h c m} = \frac{v}{2 c} = \frac{1}{4}$

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