(b) What is the energy of one of these photons?

Verified step by step guidance

1. insert step 1> Identify the formula to calculate the energy of a photon, which is given by the equation: E = h \cdot f, where E is the energy of the photon, h is Planck's constant (6.626 \times 10^{-34} \text{ J} \cdot \text{s}), and f is the frequency of the photon.
2. insert step 2> If the frequency (f) is not provided, use the relationship between frequency and wavelength: c = \lambda \cdot f, where c is the speed of light (3.00 \times 10^8 \text{ m/s}) and \lambda is the wavelength. Rearrange this equation to solve for frequency: f = \frac{c}{\lambda}.
3. insert step 3> Substitute the value of the wavelength (\lambda) into the equation from step 2 to find the frequency (f) of the photon.
4. insert step 4> Substitute the calculated frequency (f) from step 3 into the energy equation from step 1: E = h \cdot f.
5. insert step 5> Calculate the energy (E) using the values of Planck's constant (h) and the frequency (f) obtained in the previous steps.

Key Concepts

Photon Energy

Photon energy is the energy carried by a single photon, which is a quantum of electromagnetic radiation. It is directly proportional to the frequency of the radiation and inversely proportional to its wavelength. The energy can be calculated using the formula E = hν, where E is energy, h is Planck's constant (6.626 x 10^-34 J·s), and ν (nu) is the frequency of the photon.

Planck's Constant

Planck's constant is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. It is a key component in the equation E = hν, where it provides the proportionality factor that allows for the conversion between the frequency of electromagnetic radiation and its energy. Understanding this constant is essential for calculating photon energy.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, ranging from radio waves to gamma rays. Each type of radiation has a specific wavelength and frequency, which determines its energy. Understanding where a photon falls within this spectrum is crucial for determining its energy, as different regions correspond to different energy levels.