What is the energy of a photon with a wavelength of 500 nm?
Practice Questions
Q1
What is the energy of a photon with a wavelength of 500 nm?
3.98 eV
2.48 eV
1.24 eV
0.62 eV
Questions & Step-by-Step Solutions
What is the energy of a photon with a wavelength of 500 nm?
Correct Answer: 3.98 eV
Step 1: Understand the formula for the energy of a photon, which is E = hc/λ.
Step 2: Identify the constants needed for the formula: h (Planck's constant) = 6.626 x 10^-34 J·s and c (speed of light) = 3 x 10^8 m/s.
Step 3: Convert the wavelength from nanometers to meters. Since 1 nm = 10^-9 m, 500 nm = 500 x 10^-9 m.
Step 4: Substitute the values into the formula: E = (6.626 x 10^-34 J·s)(3 x 10^8 m/s) / (500 x 10^-9 m).
Step 5: Calculate the numerator: (6.626 x 10^-34)(3 x 10^8) = 1.9878 x 10^-25 J·m.
Step 6: Calculate the energy: E = (1.9878 x 10^-25 J·m) / (500 x 10^-9 m) = 3.9756 x 10^-19 J.
Step 7: Convert the energy from joules to electronvolts (eV). Use the conversion 1 eV = 1.602 x 10^-19 J. So, E = (3.9756 x 10^-19 J) / (1.602 x 10^-19 J/eV) = 2.48 eV.
