Question

In a photoelectric effect experiment, a laser beam of unknown wavelength is shone on a cesium photo cathode (work function of \(\phi=2.100 \mathrm{eV}\) ). It is found that a stopping potential of \(0.310 \mathrm{~V}\) is needed to eliminate the current. Next, the same laser is shone on a photo cathode made of an unknown material, and a stopping potential of \(0.110 \mathrm{~V}\) is needed to eliminate the current. a) What is the work function for the unknown material? b) What metal is a possible candidate for the unknown material?

Short answer

Question: Calculate the work function for the unknown photo cathode and identify the possible metal for the unknown material based on the given stopping potentials for cesium and the unknown photo cathodes. Answer: To calculate the work function for the unknown photo cathode, follow the given steps: 1. Calculate the kinetic energy of electrons for the cesium photo cathode using the provided stopping potential. 2. Calculate the energy of the incident light using the work function of cesium and the kinetic energy calculated in step 1. 3. Calculate the kinetic energy of electrons for the unknown photo cathode using the provided stopping potential. 4. Calculate the work function of the unknown photo cathode using the energy of the incident light and the kinetic energy calculated in step 3. After finding the work function of the unknown photo cathode, compare it with the known work functions of different metals. The metal with a work function that matches (or is very close to) the calculated work function might be a candidate for the unknown material.

Step-by-step solution

Calculate the Kinetic Energy of Electrons for Cesium Photo Cathode

Using the given stopping potential (\(V_s\)) for the cesium photo cathode, we can calculate the kinetic energy of the emitted electrons: $$ E_k = eV_s $$ Given: \(V_s = 0.310 \mathrm{V}\) and \(e = 1.602 \times 10^{-19} \mathrm{C}\) $$ E_k = (1.602 \times 10^{-19} \mathrm{C})(0.310 \mathrm{V}) $$

Calculate the Energy of the Incident Light

Using the formula mentioned in the analysis, we can find the energy of the incident light: $$ E_k = hf - \phi $$ Given: \(\phi_{Cs} = 2.100 \mathrm{eV}\) Where \(\phi_{Cs}\) is the work function of Cesium. Since we need the energy in electronvolt (eV), convert the kinetic energy from Joules to electronvolt by dividing by \(e\): $$ hf - \phi_{Cs} = E_k/e $$ $$ hf = E_k/e + \phi_{Cs} $$

Calculate the Kinetic Energy of Electrons for Unknown Photo Cathode

Using the given stopping potential (\(V_s\)) for the unknown photo cathode, we can calculate the kinetic energy of the emitted electrons: $$ E_k' = eV_s' $$ Given: \(V_s' = 0.110 \mathrm{V}\) and \(e = 1.602 \times 10^{-19} \mathrm{C}\) $$ E_k' = (1.602 \times 10^{-19} \mathrm{C})(0.110 \mathrm{V}) $$

Calculate the Work Function of the Unknown Photo Cathode

Now, using the formula mentioned in the analysis, we can find the work function of the unknown photo cathode: $$ E_k' = hf - \phi' $$ Where \(\phi'\) is the work function of the unknown material. Since we have found the energy of the incident light, we can calculate \(\phi'\): $$ \phi' = hf - E_k'/e $$ Now, plug the values you found and calculate the work function \(\phi'\). #b) Identify the possible metal for the unknown material#

Compare the calculated work function with the known work functions

Compare the calculated work function with the known work functions of different metals. The metal with a work function that matches (or is very close to) the calculated work function might be a candidate for the unknown material. You can use a table of work functions of different metals for this comparison.