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) = \bigl(0.500 ,\, 2.43\times10^{-3}\,\text{nm}\bigr)

, where

x = (1-\cos\theta)

(dimensionless) and

y = \Delta\lambda

(nm). Assume the scattering centers are free electrons at rest. Take the speed of light to be

c = 3.00\times10^{8}\,\text{m}\,\text{s}^{-1}

and the electron rest mass to be

m_{e}=9.11\times10^{-31}\,\text{kg}

. (a) Determine a value for Planck’s constant

h

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\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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