Question

Light with a wavelength of 190 nm is incident on a metal surface. The most energetic electrons emitted from the surface are measured to have 4.0 ev of kinetic energy. Which of the metals in the table is the surface most likely to be made of?

Answer 1

Answer:

The surface is most likely to be made of Sodium.

Explanation:

Firstly, we determine the threshold wavelength and the work function of the metal by using Einstein's Photoelectric Equation.

Einstein's Photoelectric Equation:

$\frac{hc}{\lambda}=\frac{hc}{\lambda^{0}}+K.E.$

$\lambda^{0}$ = threshold wavelength

$\lambda$ = wavelength = 190 nm = $190\times10^{-9}m$

K.E. = the kinetic energy of the emitted electrons = 4.0 eV = $6.4\times10^{-19}$

By substituting the above numbers in the equation, the threshold wavelength of the metal can be found:

$\lambda^{0}$ = $490.2\times10^{-9}m$ = 490.2 nm

The work function = $\frac{hc}{\lambda^{0}}$ = $\frac{6.626\times10^{-34}\times3\times10^{8}}{490.2\times10^{-9}\times1.6\times10^{-19}}$ = 2.534 eV

The metal with which the surface of the table is made can be determined by the work function.

The above work function is most close to that of Sodium which has a work function of 2.38 eV

Therefore, the surface of the table is most likely to be made of Sodium.