Question

If the maximum energy given to an electron during compton scattering is 30 kev, what is the wavelength of the incident photon?

Answer 1

The wavelength of the incident photon is $1.19x10^{-2} nm$.

What is wavelength?

The wavelength, or the distance over which the shape of a periodic wave repeats, is the spatial period in physics. It is a property of both traveling waves and standing waves, as well as other spatial wave patterns. It is the distance between two successive corresponding locations of the same phase on the wave, such as two neighboring crests, troughs, or zero crossings. The Greek letter lambda is frequently used to denote wavelength. The term wavelength is also sometimes used to describe modulated waves, their sinusoidal envelopes, or waves created by the interference of several sinusoids.

The relationship between wavelength and frequency is inverse, assuming a sinusoidal wave flowing at a constant speed.

Calculations:

The energy loss Δλ=h/$m_{e} c$(1-cos∅)

Conservation of momentum gives,

$h_{f} =P_{e} c-hf'\\hf+hf'=P_{e} c\\hf+hf'=\sqrt{(m_{e} c^{2} } +k^{2} )-me^{2} c^{4} \\\\=\sqrt {(511+30)^{2} -(511)^{2} } \\=178keV$

$hf=hf'+k=hf-hf'=30keV$

$2hf=178+30\\2hf=208\\hf=104keV$

Wavelength(λ)=$\frac{hc}{104keV}$=$\frac{1.24keV.nm}{104keV}$

Wavelength(λ)=$1.19x10^{-2} nm$

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