First slide

Matter waves (DC Broglie waves)

Question

The De Broglie wavelength of a particle is equal to that of a photon, then the energy of photon will be

Moderate

A

equal to the kinetic energy of the particle
B

less than the kinetic energy of particle
C

equal to the total energy of the particle
D

more than the kinetic energy of the particle

Solution

$f o r p a r t i c l e λ = \frac{h}{m v} f o r p a r t i c l e, e n e r g y E_{p a} = \frac{1}{2} m v^{2} f o r p h o t o n λ_{p h} = \frac{h}{m_{p h} c} f o r p h o t o n, e n e r g y E_{p h} = m_{p h} c^{2} A s λ_{p h} = λ_{p a} \Rightarrow m_{p h} c = m v N o w \frac{E_{p h}}{E_{p a}} = \frac{m_{p h} c^{2}}{\frac{1}{2} m v^{2}} = \frac{(m_{p h} c) c}{\frac{1}{2} (m v) v} = \frac{2 c}{v} > 1 \Rightarrow E_{p h} > E_{p a}$

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