## Saturday, January 31, 2015

### Photo Electric Effect Problems and Solutions

The phenomenon of emission of electrons from a metal surface when a light of suitable frequency incident of the metal surface is called photo electric effect.

Problem and solution

A metal of work function of 4 electron volts is exposed to radiation of the wavelength 140 nm. What is the corresponding stopping potential?

We can solve this problem basing on the very definition of energy. It is written basing on plank’s quantum concept. We can further write photo electric equation to solve the problem as shown below.

Problem and solution

On the cathode of a photoelectric cell two different wavelengths of light are allowed to incident. The work function of the metal surface is given. A uniform magnetic field of known magnetic field strength is applied perpendicular to the cell. Find the radius of circular path described by the photo electrons?

To solve this problem, first of all we have to analyse whether the incident light is sufficient enough energy for the emission of photo electrons or not.

It is mathematically observed that photo electric effect is possible only with the first wavelength but not with the second wavelength. It is simply because the wavelength and the second case is more than the threshold wavelength.

We shall also know that whenever a magnetic field is applied perpendicular plane, the charged particle like electron takes a circular path and the necessary centripetal forces provided by the force due to the magnetic field on the charger particles.

The problem is solved as shown below.

Problem and solution

If the wavelength of the incident radiation changes from one value to other value, the corresponding kinetic energy emitted by the photo electrons also changes from one value to other value. What is the work function of the metal surface?

In solving this problem, we can use photo electric equation. According to this equation the total energy supplied by the photo is equal to sum of work function and the kinetic energy of the electron. By applying this condition for both the cases and by simplifying the equation we can derive the equation further work function as shown below.

Problem and solution

For a certain metal threshold frequency is given. When the incident frequency is doubled the threshold frequency, electrons comes out with a certain velocity. If the incident frequency is five times threshold frequency, what is the velocity with which the electrons come out?

We can solve this problem also basing on photo electric equation. We know that the kinetic energy of the electron emitted is equal to the difference between the energy of the incident photon and the work function. By substituting this condition for both the cases, cases that are given in the problem, we can solve it.

Problem and solution

Photo electric effect from a metallic surface is observed from two different frequencies where first frequency is greater than that of the second frequency. If the ratio of the maximum kinetic energy emitted by the photo electrons in both the cases is given, find the threshold frequency of the metal surface?

We know that the incident energy of the photon is equal to sum of work function and the kinetic energy. Applying this concept for both the frequencies that are given, we can calculate the threshold frequency as shown below.

Problem and solution

A photon of known energy ejects photo electrons from metal surface with a certain work function. If this emitted electron enters into a uniform magnetic field of known induction perpendicular to the field, what is the radius of the circular path taken by it?

As the total energy of the photon is equal to sum of work function and kinetic energy, we can write the equation for the velocity of the ejected electron as shown below. This electron that is entering into the magnetic field perpendicularly shall experience a centripetal force and shall take a circular path. The necessary centripetal forces provided by the force experienced by the electron due to the magnetic field.

Problem and solution

When a light of known wavelength incident on a photoelectric surface, the velocity of the fastest electron emitted is  V . If the incident wavelength is 75% of the initial wavelength, what will be the velocity of the emitted electron?

We can solve this problem basing on photo electric equation. According to this equation the total energy supplied by the light in the form of photon, is equal to sum of work function as well as the kinetic energy of emitted electron. By substituting the given values in this equation, we can get to equations. By solving that to equations we can identify the relation between the last of the electron in the second case with respect to the velocity of the electron in the first case.

Problem and solution

Here we are going to solve a simple problems basing on photo electric effect.

When a radiation of certain wavelength is incident on a metallic surface, the stopping potentially is found to be 4.8 V. If the same surface is illuminated by the radiation of double the wavelength, the stopping potential is found to be 1.6 V. What is the threshold wavelength of the surface?

We can solve this problem basing on Einstein’s  photo electric equation. According to this equation the total energy supplied by the photon is equal to sum of work function and kinetic energy. By applying the given data in this equation in two different cases and by simplifying the equation is we can solve the problem as shown below.

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