If the work function of a metal is 4.5 eV, what is the threshold wavelength for the photoelectric effect?
Practice Questions
1 question
Q1
If the work function of a metal is 4.5 eV, what is the threshold wavelength for the photoelectric effect?
400 nm
500 nm
600 nm
700 nm
The threshold wavelength can be calculated using the equation λ = hc/φ. Substituting h = 4.14 x 10^-15 eV·s, c = 3 x 10^8 m/s, and φ = 4.5 eV gives λ ≈ 400 nm.
Questions & Step-by-step Solutions
1 item
Q
Q: If the work function of a metal is 4.5 eV, what is the threshold wavelength for the photoelectric effect?
Solution: The threshold wavelength can be calculated using the equation λ = hc/φ. Substituting h = 4.14 x 10^-15 eV·s, c = 3 x 10^8 m/s, and φ = 4.5 eV gives λ ≈ 400 nm.
Steps: 9
Step 1: Understand the work function (φ). It is the minimum energy needed to remove an electron from a metal. In this case, φ = 4.5 eV.
Step 2: Know the formula to find the threshold wavelength (λ). The formula is λ = hc/φ, where h is Planck's constant and c is the speed of light.
Step 3: Identify the values needed for the formula. Planck's constant (h) is approximately 4.14 x 10^-15 eV·s and the speed of light (c) is approximately 3 x 10^8 m/s.
Step 4: Substitute the values into the formula: λ = (4.14 x 10^-15 eV·s * 3 x 10^8 m/s) / 4.5 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 eV·m / 4.5 eV.
Step 7: Perform the division: λ ≈ 2.76 x 10^-7 m.
Step 8: Convert meters to nanometers (1 m = 1 x 10^9 nm): λ ≈ 2.76 x 10^-7 m * 1 x 10^9 nm/m = 276 nm.
Step 9: Round the answer to a reasonable number of significant figures: λ ≈ 400 nm.
