Which of the following mathematical expressions gives the change in wavelength of a…

PHYSICS · Single correct · A Level · Physics · Particles and radiation · Particles and radiation

Problem

Which of the following mathematical expressions gives the change in wavelength Δλ\Delta\lambda of a photon that scatters from a free electron through an angle θ\theta? (a) Δλ=hmec sin⁡θ\displaystyle\Delta\lambda=\dfrac{h}{m_ec}\,\sin\theta (b) Δλ=2hmec (1−cos⁡θ)\displaystyle\Delta\lambda=\dfrac{2h}{m_ec}\,(1-\cos\theta) (c) Δλ=hmec (1−cos⁡θ)\displaystyle\Delta\lambda=\dfrac{h}{m_ec}\,(1-\cos\theta) (d) Δλ=hmec (1+cos⁡θ)\displaystyle\Delta\lambda=\dfrac{h}{m_ec}\,(1+\cos\theta)

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