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Photon energy is a central concept in understanding the photoelectric effect. It refers to the energy carried by a single photon, which is a quantum of electromagnetic radiation. To calculate the energy of a photon, we use the formula:

• \[ E = \frac{hc}{\lambda} \]
• Where \( h \) is Planck's constant \((6.626 \times 10^{-34} \text{ J s})\), \( c \) is the speed of light \((3 \times 10^8 \text{ m/s})\), and \( \lambda \) is the wavelength of the incident light.

In the given problem, the wavelength is \(200 \text{ nm}\) or \(200 \times 10^{-9} \text{ m}\). Substituting these values in, the energy of a photon hitting the aluminum surface was calculated to be approximately \(6.20 \text{ eV}\). This energy represents how much potential influence the photon has to cause an effect when it interacts with matter, like ejecting electrons.

Kinetic energy is the energy that an object possesses due to its motion. In the context of the photoelectric effect, when photons strike a metal surface, electrons are ejected, gaining kinetic energy in the process. The maximum kinetic energy of the ejected electrons can be calculated using:

• \[ KE_{max} = E_{photon} - W \]
• Where \( E_{photon} \) is the energy of the incident photon and \( W \) is the work function of the material (aluminum in this case).

The work function is the minimum energy required to eject an electron from the surface. In our example, the photon energy is \(6.20 \text{ eV}\) and the work function of aluminum is \(4.20 \text{ eV}\). Thus, the maximum kinetic energy of the electrons is \(2.00 \text{ eV}\). For the slowest ejected electrons, the kinetic energy can theoretically be zero if all the photon energy is used up in overcoming the work function.

Stopping potential is the voltage required to stop the most energetic ejected electrons from reaching the other side of the photoelectric cell. It directly measures the maximum kinetic energy of the electrons emitted. The relationship between stopping potential and kinetic energy is given by:

• \[ KE = eV_0 \]
• Where \( KE \) is kinetic energy and \( V_0 \) is the stopping potential, with \( e \) as the elementary charge.

In this problem, the maximum kinetic energy was found to be \(2.00 \text{ eV}\), translating to a stopping potential \( V_0 \) of \(2.00 \text{ V}\). This provides insight into the energies of electrons ejected by the photon and helps in understanding the efficiency of the photoelectric effect in various applications.

The cutoff wavelength is a critical parameter in photoelectron emission. It refers to the longest wavelength of incident light that can effectively eject electrons from a metal surface. At this wavelength, the energy of the photons just barely overcomes the work function, leaving no extra energy to be converted into kinetic energy for the electrons.

• \[ \frac{hc}{\lambda_c} = W \]
• Where \( \lambda_c \) is the cutoff wavelength, \( W \) is the work function, and the formula equates to zero kinetic energy of the electrons.

For aluminum, using a work function of \(4.20 \text{ eV}\), the cutoff wavelength comes out to about \(295 \text{ nm}\). This means any photon with a wavelength longer than \(295 \text{ nm}\) won't have sufficient energy to eject electrons from the aluminum surface.