Multiple Choice
Which of the following best describes the relationship between the energy (E) of a photon and its frequency (ν)?
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9. Quantum Mechanics
The Energy of Light
Multiple Choice
What is the energy, in joules, of a single photon with a wavelength of 400.0 nm?
A
4.97 \(\times\) 10^{-19} \(\text{ J}\)
B
7.45 \(\times\) 10^{-18} \(\text{ J}\)
C
2.48 \(\times\) 10^{-20} \(\text{ J}\)
D
3.10 \(\times\) 10^{-19} \(\text{ J}\)
Verified step by step guidance1
Identify the formula that relates the energy of a photon to its wavelength: \(E = \frac{hc}{\lambda}\), where \(E\) is the energy of the photon, \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength.
Write down the known constants: Planck's constant \(h = 6.626 \times 10^{-34} \text{ J}\cdot\text{s}\) and the speed of light \(c = 3.00 \times 10^{8} \text{ m/s}\).
Convert the given wavelength from nanometers to meters because SI units must be consistent: \(400.0 \text{ nm} = 400.0 \times 10^{-9} \text{ m}\).
Substitute the values of \(h\), \(c\), and \(\lambda\) into the formula \(E = \frac{hc}{\lambda}\) to set up the calculation for the energy of the photon.
Perform the division and multiplication carefully to find the energy \(E\) in joules, which will give the energy of a single photon with the given wavelength.
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