A light ray has a wavelength that is 835 µm contains 6.32 x 10^-3 J of energy. How many photons does this light ray have?

• A. 7.98 x 10¹⁸ photons
• B. 4.85 x 10¹⁹ photons
• C. 9.48 x 10¹⁸ photons
• D. 2.65 x 10¹⁹ photons

Answer: (D)

Verified step by step guidance

1. First, understand that 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 \( (6.626 \times 10^{-34} \text{ J s}) \), \( c \) is the speed of light \( (3.00 \times 10^8 \text{ m/s}) \), and \( \lambda \) is the wavelength of the light in meters.
2. Convert the given wavelength from micrometers to meters. Since 1 micrometer (µm) is \( 1 \times 10^{-6} \) meters, the wavelength \( \lambda = 835 \text{ µm} \) is equivalent to \( 835 \times 10^{-6} \text{ m} \).
3. Substitute the values of \( h \), \( c \), and \( \lambda \) into the equation \( E = \frac{hc}{\lambda} \) to calculate the energy of a single photon.
4. Once you have the energy of a single photon, use the total energy provided (6.32 x 10^-3 J) to find the number of photons. This can be done by dividing the total energy by the energy of a single photon: \( \text{Number of photons} = \frac{\text{Total energy}}{E} \).
5. Perform the division to find the number of photons, ensuring that your units are consistent and that you handle the powers of ten correctly.