Question

The wavelength you entered in the last problem is related to the energy required to eject an electron from sodium metal, the so-called work function. Use the relationship between photon wavelength and energy to calculate the work function of sodium (in electron-Volts) based on your measurement in the last problem.

Answer 1

Answer:

2.30 eV

Explanation:

Some details of the problem are missing:

"Light of wavelength 540 nm is required to extract electrons from sodium. What is the work function of sodium?"

The equation that describes the photoelectric effect is

$\frac{hc}{\lambda}=\phi +K$

where:

$\frac{hc}{\lambda}$ is the energy of the incoming photon, with

$h=6.63\cdot 10^{-34} Js$ is Planck constant

$c=3.0\cdot 10^8 m/s$ is the speed of light

$\Phi$ is the work function of the material

K is the maximum kinetic energy of the emitted photoelectrons

The minimum energy needed by the photons to extract the photoelectrons is that for which the kinetic energy is zero, so

K = 0

Therefore we have

$\frac{hc}{\lambda}=\phi$

In this problem, we know that the wavelength of the incoming light is

$\lambda=540 nm = 540\cdot 10^{-9}m$

Therefore, we can find the work function of sodium:

$\phi=\frac{hc}{\lambda}=\frac{(6.63\cdot 10^{-34})(3\cdot 10^8)}{540\cdot 10^{-9}}=3.68\cdot 10^{-19}J$

And converting into electronvolts,

$\phi=\frac{3.68\cdot 10^{-19}J}{1.6\cdot 10^{-19}}=2.30 eV$