Question

The work function of a metal surface is 4.80 x 10⁻¹⁹ J. The maximum speed of the emitted electrons is va = 730 km/s when the wavelength of the light is λA. However, a maximum speed of vB = 500 km/s is observed when the wavelength is λB. Find the wavelengths.

Answer 1

The work function of a metal surface represents the minimum amount of energy needed to remove an electron. The maximum speed of emitted electrons can be found by subtracting the work function from the energy of the photon. Using the given values, the wavelengths corresponding to two different maximum speeds can be calculated.

Step-by-step explanation:

The work function of a metal surface represents the minimum amount of energy that is needed to remove an electron from the surface of the metal. In this case, the work function is given as 4.80 x 10⁻¹⁹ J. The maximum speed of the emitted electrons, or the kinetic energy, can be determined using the equation:

Kinetic Energy (K) = Energy of the photon (E) - Work Function (W)

Substituting the values given in the question, we can solve for the two wavelengths:

1. For the maximum speed of 730 km/s, we have:
   730 km/s = c × λA (where c is the speed of light)
   Solving for λA gives us a wavelength of 410 nm.
2. For the maximum speed of 500 km/s, we have:
   500 km/s = c × λB
   Solving for λB gives us a wavelength of 590 nm.