Question

A metal surface is susceptible to a photoelectric threshold frequency of 8.529*10>14Hz. Will the monochromatic UV light sources of wavelengths 283 nm, 342 nm, and 363 nm be able to eject photoelectrons from the metal. If so what is the speed of the fastest electron ejected?

Answer 1

Threshold frequency = 8.529 *10¹⁴ Hz

Since, c = wavelength * frequency

or, threshold wavelength = 3 * 10⁸ m/s /  8.529 *10¹⁴ Hz = 351.74 nm

Wavelengths less than this value will be able to eject electrons.

So, only 283 nm and 342 nm wavelength will be able to eject electrons.

From photoelectric effect equation.

Energy of a photon = Work function + Maximum Kinetic Energy

Since, E = hc/wavelength

where h = planck's constant = 6.626* 10^-34 J-s

So, Work function = (6.626* 10^-34 J-s * 3 * 10⁸ m/s)/ threshold wavelength

   = (6.626* 10^-34 J-s * 3 * 10⁸ m/s)/ 351.74 nm = 5.65 * 10^-19 J

Energy of 283 nm wavelength = hc/363 nm = (6.626* 10^-34 J-s * 3 * 10⁸ m/s)/ 283 nm

   = 7.02 * 10^-19 J

Energy of 342 nm wavelength = hc/342 nm = (6.626* 10^-34 J-s * 3 * 10⁸ m/s)/ 342 nm

= 5.81 * 10^-19 J

Since, Energy of the 283 nm wavelength is highest, so electron released in this case will have the maximum kinetic energy

Thus, Maximum Kinetic energy of electron for 283 nm = 7.02 * 10^-19 J - 5.65 * 10^-19 J

= 1.37 * 10^-19 J

Since, 1/2 * m * v² = 1.37 * 10^-19 J

or, m = mass of electron = 9.1 * 10^-31 Kg

or, v = ( 2 * 1.37 * 10^-19 J / 9.1 * 10^-31 Kg )^-1/2 = 5.48 * 10⁵ m/s

Now, Maximum Kinetic energy of electron for 342 nm = 5.81 * 10^-19 J - 5.65 * 10^-19 J = 0.16 * 10^-19 J

So, v = ( 2 * 0.16 * 10^-19 J / 9.1 * 10^-31 Kg )^-1/2 = 1.87 * 10⁵ m/s