Multiple Choice
Which example involves the transformation of chemical energy directly into light energy?
9. Quantum Mechanics
The Energy of Light
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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
Verified step by step guidance1
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.
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 \( 835 \times 10^{-6} \text{ m} \).
Substitute the values of \( h \), \( c \), and \( \lambda \) into the equation \( E = \frac{hc}{\lambda} \) to calculate the energy of a single photon.
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: \( \text{Number of photons} = \frac{\text{Total energy}}{E} \).
Perform the division to find the number of photons, ensuring that your units are consistent and that you handle the powers of ten correctly.
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