How many photons are contained in a flash of green light (525 nm) that contains 189 kJ of energy?

• A. 2.34 x 10^18 photons
• B. 4.58 x 10^20 photons
• C. 3.12 x 10^19 photons
• D. 5.67 x 10^21 photons

Answer: (B)

Verified step by step guidance

1. First, understand the relationship between energy, wavelength, and the number of photons. The energy of a single photon can be calculated using the equation: E = \( \frac{hc}{\lambda} \), where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and \( \lambda \) is the wavelength of the light.
2. Convert the wavelength from nanometers to meters. Since 1 nm = 1 x 10^-9 m, the wavelength \( \lambda \) = 525 nm = 525 x 10^-9 m.
3. Calculate the energy of a single photon using the formula: E = \( \frac{(6.626 \times 10^{-34} \text{ J·s})(3.00 \times 10^8 \text{ m/s})}{525 \times 10^{-9} \text{ m}} \). This will give you the energy in joules for one photon of green light.
4. Determine the total number of photons by dividing the total energy of the flash by the energy of a single photon. Use the formula: Number of photons = \( \frac{189 \text{ kJ}}{E} \). Remember to convert 189 kJ to joules (1 kJ = 1000 J) before performing the division.
5. Perform the division to find the number of photons. This will give you the total number of photons contained in the flash of green light.