A research group wishes to model how the maximum speed of photoelectrons from a…

PHYSICS · Multi-part · CBSE · Physics · Dual Nature of Radiation and Matter · Dual Nature of Radiation and Matter

Problem

A research group wishes to model how the maximum speed of photoelectrons from a particular metal depends on the wavelength of incident light. The metal has a work function of

3.20\,\text{eV}

. Electrons may be treated as non-relativistic provided their speed is less than

0.10\,c

. Constants:

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

h = 6.63\times10^{-34}\,\text{J}\,\text{s}

e = 1.60\times10^{-19}\,\text{C}

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

. (a) Derive an expression for the maximum speed

v_{\text{max}}

of emitted electrons as a function of incident wavelength

\lambda

. (b) Using your expression, compute

v_{\text{max}}

for

\lambda = 300\,\text{nm}

. (c) Determine the longest wavelength

\lambda_{\text{NR}}

for which the non-relativistic approximation (

v_{\text{max}} < 0.10\,c

) remains valid for this metal.

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