(a) Calculate and compare the energy of a photon with a wavelength of 3.0 mm to that of a photon with a wavelength of 0.3 nm.

Verified step by step guidance

1. Step 1: Understand the relationship between the energy of a photon and its wavelength using the formula: \( E = \frac{hc}{\lambda} \), 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 photon.
2. Step 2: Convert the given wavelengths into meters to ensure consistency in units. For the first photon, convert 3.0 mm to meters (1 mm = 1 \times 10^{-3} m). For the second photon, convert 0.3 nm to meters (1 nm = 1 \times 10^{-9} m).
3. Step 3: Calculate the energy of the first photon using its wavelength in meters. Substitute the values of \( h \), \( c \), and the converted wavelength into the energy formula.
4. Step 4: Calculate the energy of the second photon using its wavelength in meters. Again, substitute the values of \( h \), \( c \), and the converted wavelength into the energy formula.
5. Step 5: Compare the energies of the two photons. Discuss how the difference in wavelength affects the energy, noting that shorter wavelengths correspond to higher energy photons.