If a metal has a work function of 2 eV, what is the threshold wavelength for the photoelectric effect?
Practice Questions
1 question
Q1
If a metal has a work function of 2 eV, what is the threshold wavelength for the photoelectric effect?
620 nm
400 nm
500 nm
300 nm
The threshold wavelength can be calculated using the equation λ = hc/W. Substituting h = 4.14 x 10^-15 eV·s, c = 3 x 10^8 m/s, and W = 2 eV gives λ = 620 nm.
Questions & Step-by-step Solutions
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Q
Q: If a metal has a work function of 2 eV, what is the threshold wavelength for the photoelectric effect?
Solution: The threshold wavelength can be calculated using the equation λ = hc/W. Substituting h = 4.14 x 10^-15 eV·s, c = 3 x 10^8 m/s, and W = 2 eV gives λ = 620 nm.
Steps: 8
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.
