A photon has twice the energy of a photon with a wavelength of 600 nm. What is the wavelength of this higher-energy photon?

• A. 150 nm
• B. 1200 nm
• C. 300 nm
• D. 600 nm

Answer: (C)

Verified step by step guidance

1. Recall the relationship between the energy of a photon and its wavelength, which is given by the equation \(E = \frac{hc}{\lambda}\), where \(E\) is energy, \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength.
2. Since the problem states that the new photon has twice the energy of a photon with a wavelength of 600 nm, express this as \(E_{new} = 2E_{600}\).
3. Using the energy-wavelength relationship, write \(E_{600} = \frac{hc}{600\ \text{nm}}\) and \(E_{new} = \frac{hc}{\lambda_{new}}\).
4. Set up the equation \(\frac{hc}{\lambda_{new}} = 2 \times \frac{hc}{600\ \text{nm}}\) and simplify by canceling \(hc\) from both sides.
5. Solve for the new wavelength \(\lambda_{new}\), which will be \(\lambda_{new} = \frac{600\ \text{nm}}{2}\), giving the wavelength of the higher-energy photon.