What is the maximum wavelength of light that can cause the photoelectric effect
Practice Questions
Q1
What is the maximum wavelength of light that can cause the photoelectric effect in a metal with a work function of 2.0 eV?
620 nm
400 nm
500 nm
300 nm
Questions & Step-by-Step Solutions
What is the maximum wavelength of light that can cause the photoelectric effect in a metal with a work function of 2.0 eV?
Correct Answer: 620 nm
Step 1: Understand the photoelectric effect. It occurs when light hits a metal and causes it to emit electrons.
Step 2: Know that each metal has a work function, which is the minimum energy needed to release an electron. In this case, the work function is 2.0 eV.
Step 3: Convert the work function from electron volts (eV) to joules (J) because we need to use SI units. Use the conversion: 1 eV = 1.6 x 10^-19 J. So, 2.0 eV = 2.0 * 1.6 x 10^-19 J = 3.2 x 10^-19 J.
Step 4: Use the formula for maximum wavelength: λ_max = hc/E, where h is Planck's constant (6.63 x 10^-34 J·s) and c is the speed of light (3 x 10^8 m/s).
Step 5: Plug in the values into the formula: λ_max = (6.63 x 10^-34 J·s * 3 x 10^8 m/s) / (3.2 x 10^-19 J).
Step 6: Calculate the numerator: 6.63 x 10^-34 * 3 x 10^8 = 1.989 x 10^-25 J·m.
Step 7: Now divide the numerator by the energy (3.2 x 10^-19 J): λ_max = 1.989 x 10^-25 J·m / 3.2 x 10^-19 J.
Step 8: Perform the division to find λ_max: λ_max = 620 nm (nanometers).
