Question

The work function of a certain material is \(5.8 \mathrm{eV}\). What is the photoelectric threshold frequency for this material?

Short answer

Answer: The photoelectric threshold frequency for this material is 1.4 x 10^15 Hz.

Step-by-step solution

Convert the work function from eV to Joules

In order to use the photoelectric effect equation, we need to have the work function in Joules. The work function is given as \(5.8\mathrm{eV}\). We can convert this to Joules using the following conversion factor: \(1\mathrm{eV} = 1.6\times10^{-19}\mathrm{J}\). So, the work function in Joules is: \(5.8\mathrm{eV}\times\frac{1.6\times10^{-19}\mathrm{J}}{1\mathrm{eV}} = 9.28\times10^{-19}\mathrm{J}\)

Use the photoelectric effect equation to find the threshold frequency

The photoelectric effect equation relates the energy of a photon to the work function and the kinetic energy of the emitted electron: \(E_{photon} = W + K\). Since we're looking for the threshold frequency, the kinetic energy of the emitted electron is zero, so \(E_{photon} = W\). The energy of a photon is given by \(E_{photon}=hf\), where \(h\) is Planck's constant (\(6.63\times10^{-34} Js\)) and \(f\) is the frequency of the photon. Since we know the work function \(W\), we can find the threshold frequency \(f\) using the equation: \(9.28\times10^{-19}\mathrm{J} = (6.63\times10^{-34} \mathrm{Js})(f)\)

Solve for the threshold frequency \(f\)

Now, we just need to solve the equation for \(f\): \(f = \frac{9.28\times10^{-19}\mathrm{J}}{6.63\times10^{-34} \mathrm{Js}} = 1.4\times10^{15}\mathrm{Hz}\) So, the photoelectric threshold frequency for this material is \(1.4\times10^{15}\mathrm{Hz}\).