If a metal has a work function of 4 eV, what is the minimum wavelength of light

If a metal has a work function of 4 eV, what is the minimum wavelength of light required to cause the photoelectric effect?

If a metal has a work function of 4 eV, what is the minimum wavelength of light required to cause the photoelectric effect?

Step 1: Understand the problem. We need to find the minimum wavelength of light that can cause the photoelectric effect for a metal with a work function of 4 eV.
Step 2: Know the formula to use. The formula to find the wavelength (λ) is λ = hc/W, where h is Planck's constant, c is the speed of light, and W is the work function.
Step 3: Identify the values needed for the formula. We have: h = 4.14 x 10^-15 eV·s, c = 3 x 10^8 m/s, and W = 4 eV.
Step 4: Substitute the values into the formula. Replace h, c, and W in the equation λ = hc/W.
Step 5: Calculate the wavelength. Perform the calculation to find λ.
Step 6: Convert the result to nanometers if necessary. Since 1 nm = 10^-9 m, convert the wavelength from meters to nanometers.

Photoelectric Effect – The phenomenon where electrons are emitted from a material when it absorbs light of sufficient energy.
Work Function – The minimum energy required to remove an electron from the surface of a metal.
Wavelength and Energy Relationship – The relationship between the energy of a photon and its wavelength, given by the equation E = hc/λ.