Question

Light from a source with a variable wavelength is incident on a metal. It is observed that electrons are emitted from the surface of the metal for all wavelengths less than 525 nm but never for wavelengths above 525 nm. (a) What is the minimum energy necessary to remove an electron from the surface of the metal? (b) After leaving the surface, electrons must cross through a potential difference v in order to contribute to the current in an external circuit. When the wavelength of the light is changed to 345 nm, what potential difference is necessary to prevent the most energetic electrons from completing the circuit?

Answer 1

The minimum energy necessary to remove an electron from the surface of a metal is called the work function. To find the minimum energy, convert the cutoff wavelength to frequency and use the equation E = hf. To find the potential difference needed to prevent the most energetic electrons from completing the circuit, use the equation V = KE/e.

Step-by-step explanation:

The minimum energy necessary to remove an electron from the surface of a metal is called the work function. The work function is equal to the energy of a photon with a wavelength equal to the cutoff wavelength. In this case, the cutoff wavelength is 525 nm. To find the minimum energy, we can convert this wavelength to frequency and then use the equation E = hf, where E is the energy, h is Planck's constant (6.626 x 10^-34 J s), and f is the frequency.

(b) When the wavelength of the light is changed to 345 nm, the potential difference needed to prevent the most energetic electrons from completing the circuit can be found using the equation V = KE/e, where V is the potential difference, KE is the kinetic energy of the electrons, and e is the charge of an electron (1.602 x 10^-19 C).