. CP Coherent light is passed through two narrow slits whose separation is 20.0 mm. The second-order bright fringe in the interference pattern is located at an angle of 0.0300 rad. If electrons are used instead of light, what must the kinetic energy(in electron volts) of the electrons be if they are to produce an interference pattern for which the second-order maximum is also at 0.0300 rad?

Coherent light is a beam of photons (almost like particles of light waves) that have the same frequency and are all at the same frequency. Only a beam of laser light will not spread and diffuse. In lasers, waves are identical and in phase, which produces a beam of coherent light.

From equation 36.13, when a beam of Wavelength A is diffracted from double slits separated by distance d, the condition of a

bright fringe is:

Where 9m is the angle of line from center of the distance betWeen the two slits to mth bright fringe on screen-

From equation 39.], the de Broglie wavelength of a particle of momentum p is given by:

Step 2 2 of 5

Givens

The distance between the slits is and the angle of the second-order bright fringe is

For the second bright fringe, m = 2-

So, we plug our values for 92 and d into equation (I), so We get the wavelength of the light:

For the electrons to produce an interference pattern for which the second-order maximum is also at 0.03007‘ad , the

electrons must have the same wavelength as that of the photon of the light

Thus, the Wavelength of the electrons is A = 3.00 X 10—7m -

Now, we plug this value into equation (2), so we get the momentum of the electrone

Step A

The nonrelativistic momentum is given by:

So, We substitute for me and 13, so we get the speed of the electrons

This speed is very small compared to the speed of light, so we use the nonrelativistic approach-

The nonrelativistic: kinetic energy is given by:

So, we substitute for me and ’0, so we get the kinetic energy of the electrons

Therefore the kinetic energy of the electron is