Two independent measurements are made on photons that scatter from free electrons…

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Modern Physics · Modern Physics

Problem

Two independent measurements are made on photons that scatter from free electrons initially at rest. For the first measurement the scattering angle is

55^{\circ}

and the scattered wavelength is

0.062\,\text{nm}

. For the second measurement the angle is

125^{\circ}

and the scattered wavelength is

0.067\,\text{nm}

. Assume the same incident beam is used for both measurements and denote its unknown wavelength by

\lambda_{0}

. (a) Write two algebraic equations that relate

\lambda_{0}

to the measured scattered wavelengths and the corresponding angles. (b) Solve the simultaneous equations to determine the numerical value of the incident wavelength

\lambda_{0}

. (c) From either equation, isolate the constant of proportionality between the wavelength shift and

1-\cos\theta

. Compute its value in picometres and compare it with the accepted electron Compton wavelength of

2.43\,\text{pm}

. (d) Discuss two possible experimental sources of uncertainty that could account for any discrepancy between your computed constant and the accepted value.

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