Upon being struck by 99.3-nm photons, a metal ejects electrons with a maximum kinetic energy of 7.53 eV. What is the work function of this metal?

Given:
- Planck's constant, $ h = 6.626 \times 10^{-34} \, \text{J·s} $
- Speed of light, $ c = 3.00 \times 10^8 \, \text{m/s} $
- Conversion factor, $ 1 \, \text{eV} = 1.60 \times 10^{-19} \, \text{J} $

The work function of the metal in the given circumstances is approximately 4.94 eV. This calculated using Einstein's Photoelectric Equation and converting energy in Joules to electron volts (eV).

Explanation:

The work function of a metal is the minimum amount of energy needed to remove an electron from the metal. This can be calculated using Einstein's Photoelectric Equation, which states that the kinetic energy of an electron ejected by a photon is equal to the energy of the photon minus the work function of the metal.

First, we need to calculate the energy of the photon. The energy of a photon (E) is given by the equation E = hc/λ, where h is Plank’s constant, c is the speed of light, and λ is the wavelength of the light. So, the energy of the 99.3-nm photon is E = (6.626 x 10^-34 J·s)(3.00 x 10^8 m/s) / (99.3 x 10^-9 m) = 2.00 x 10^-18 J.

To convert this into eV (electron volts), we divide by the charge of an electron, which is 1.60 x 10^-19 J/eV. The energy of the photon in eV is about 12.47 eV.

Using this information, we can now calculate the work function (ϕ) using the equation: kinetic energy = energy of photon - work function. That gives us: 7.53 eV = 12.47 eV - ϕ. Solving for ϕ, we find that the work function of the metal is approximately 4.94 eV.

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