Physics

Problem

Electrons in a dilute gas cell are used as effective "free" targets for scattering experiments. A student aligns a beam of ultraviolet photons of wavelength

2.47\times10^{-8}\,\text{m}

along the

+x

axis and records both the scattered photons and recoil electrons. During analysis, the student notices that whenever a photon is detected at

90^{\circ}

above the

+x

axis (i.e., along

+y

), the associated electron is found at an angle slightly below the

-y

direction. (a) Describe qualitatively, in words, why the electron cannot be detected exactly opposite the scattered photon’s direction (i.e., at

-y

) when the photon scatters at

+y

. Your explanation should reference fundamental conservation principles. (b) Using vector arguments, explain how measurement of the electron’s angle allows one to determine whether the initial photon wavelength is shorter or longer than a critical value. Outline the reasoning without performing a calculation.

Intuitive explanation

This is Compton scattering, where a photon collides with an electron and both scatter away—but momentum and energy must be conserved simultaneously. The key insight is that when the photon scatters at 90°, it loses energy (and thus gains wavelength), so the electron must recoil at a specific angle to balance the momentum in both $x$ and $y$ directions. The "slightly below $-y$ " observation tells you the electron carries the $x$ -component of momentum the photon lost, making this a perfect setup to verify conservation laws and measure the photon's wavelength shift.

Intuitive explanation

Browse the problem library