Question

Multiple-Concept Example 3 reviews the concepts necessary to solve this problem. Radiation with a wavelength of 238 nm shines on a metal surface and ejects electrons that have a maximum speed of 3.75 × 105 m/s. Which one of the following metals is it, the values in parentheses being the work functions: potassium (2.24 eV), calcium (2.71 eV), uranium (3.63 eV), aluminum (4.08 eV), or gold (4.82 eV)?

Answer 1

Answer:

The answer is gold (4.82 eV).

Explanation:

The kinetic energy of the electron is

$K_{E} =\frac{1}{2} mv^{2} =\frac{1}{2} *9.1x10^{-31} *(3.75x10^{5} )^{2} =6.63x10^{-34} J$ = 0.4 eV

The energy of the electron is

$E=\frac{hc}{L} =\frac{6.63x10^{-34}*3x10^{8} }{238x10^{-9} } =8.35x10^{-19} J=5.22eV$

The work function is

W = E - KE = 5.22 - 0.4 = 4.82 eV

according to the result, it corresponds to gold.