If a metal has a work function of 2 eV, what is the threshold wavelength for the

If a metal has a work function of 2 eV, what is the threshold wavelength for the photoelectric effect?

If a metal has a work function of 2 eV, what is the threshold wavelength for the photoelectric effect?

Step 1: Understand the work function (W). It is the minimum energy needed to remove an electron from the metal. In this case, W = 2 eV.
Step 2: Know the equation to find the threshold wavelength (λ): λ = hc/W.
Step 3: Identify the constants needed for the equation: h (Planck's constant) = 4.14 x 10^-15 eV·s and c (speed of light) = 3 x 10^8 m/s.
Step 4: Substitute the values into the equation: λ = (4.14 x 10^-15 eV·s * 3 x 10^8 m/s) / 2 eV.
Step 5: Calculate the numerator: 4.14 x 10^-15 * 3 x 10^8 = 1.242 x 10^-6 eV·m.
Step 6: Divide the result by the work function: λ = 1.242 x 10^-6 m / 2 = 6.21 x 10^-7 m.
Step 7: Convert meters to nanometers: 6.21 x 10^-7 m = 621 nm.
Step 8: Conclude that the threshold wavelength for the photoelectric effect is 620 nm.

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.
Threshold Wavelength – The maximum wavelength of light that can cause the photoelectric effect, related to the work function.
Planck's Equation – The relationship between energy, wavelength, and frequency, given by E = hc/λ.