A student plots experimental data for photon scattering and obtains a best-fit line…

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

Problem

A student plots experimental data for photon scattering and obtains a best-fit line described verbally as follows: • The line passes through the origin and the point (x,y)=(0.500, 2.43×10−3 nm)(x,y) = \bigl(0.500 ,\, 2.43\times10^{-3}\,\text{nm}\bigr), where x=(1−cos⁡θ)x = (1-\cos\theta) (dimensionless) and y=Δλy = \Delta\lambda (nm). Assume the scattering centers are free electrons at rest. Take the speed of light to be c=3.00×108 m s−1c = 3.00\times10^{8}\,\text{m}\,\text{s}^{-1} and the electron rest mass to be me=9.11×10−31 kgm_{e}=9.11\times10^{-31}\,\text{kg}. (a) Determine a value for Planck’s constant hh implied by the slope of the student’s graph. Show your work and include correct SI units. (b) The currently accepted value of Planck’s constant is 6.63×10−34 J ⁣⋅ ⁣s6.63\times10^{-34}\,\text{J}\!\cdot\!\text{s}. Calculate the percent error of the student’s result and state whether the experimental value is an overestimate or an underestimate.

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