In an experiment to study the photoelectric effect, a scientist measures the kinetic energy of ejected electrons as a function of the frequency of radiation hitting a metal surface. She obtains the following plot. The point labeled 'n0' corresponds to light with a wavelength of 542 nm. (a) What is the value of n0 in s - 1?

Verified step by step guidance

1. Identify the given wavelength (λ) of light, which is 542 nm.
2. Convert the wavelength from nanometers to meters by multiplying by 10^-9.
3. Use the speed of light equation, c = λν, where c is the speed of light (3.00 x 10^8 m/s), λ is the wavelength in meters, and ν is the frequency in s^-1.
4. Rearrange the equation to solve for the frequency (ν): ν = c / λ.
5. Substitute the values for c and λ into the equation to find the frequency ν.

Key Concepts

Photoelectric Effect

The photoelectric effect refers to the phenomenon where electrons are emitted from a material (usually a metal) when it is exposed to light of sufficient frequency. This effect demonstrates the particle nature of light, as photons must have enough energy to overcome the work function of the material to eject electrons.

Frequency and Wavelength Relationship

The frequency (ν) and wavelength (λ) of electromagnetic radiation are inversely related through the equation c = νλ, where c is the speed of light. This means that as the wavelength increases, the frequency decreases, and vice versa. Understanding this relationship is crucial for converting the given wavelength of light into frequency for calculations.

Kinetic Energy of Ejected Electrons

The kinetic energy (KE) of ejected electrons in the photoelectric effect can be calculated using the equation KE = hν - φ, where h is Planck's constant, ν is the frequency of the incident light, and φ is the work function of the metal. This relationship highlights how the energy of the incoming photons is converted into the kinetic energy of the emitted electrons.