(a) Calculate the energy of a photon of electromagnetic radiation whose frequency is 2.94 × 10¹⁴ s^-1.

Verified step by step guidance

1. Identify the given frequency of the electromagnetic radiation, which is \(2.94 \times 10^{14} \, \text{s}^{-1}\).
2. Recall the formula for the energy of a photon, which is given by Planck's equation: \(E = h \nu\), where \(E\) is the energy of the photon, \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J} \cdot \text{s}\)), and \(\nu\) is the frequency of the radiation.
3. Substitute the given frequency and the value of Planck's constant into the equation.
4. Perform the multiplication to calculate the energy in joules (J).
5. Interpret the result, understanding that the energy calculated represents the energy carried by a single photon of the given electromagnetic radiation.

Key Concepts

Photon Energy

The energy of a photon is directly proportional to its frequency and can be calculated using the equation E = hν, where E is energy, h is Planck's constant (6.626 x 10^-34 J·s), and ν is the frequency in hertz. This relationship shows that higher frequency photons carry more energy.

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, and its value is approximately 6.626 x 10^-34 J·s. Understanding this constant is essential for calculating photon energy.

Frequency of Electromagnetic Radiation

Frequency refers to the number of cycles of a wave that pass a point in one second, measured in hertz (Hz). In the context of electromagnetic radiation, frequency is inversely related to wavelength, and it plays a crucial role in determining the energy of the photon, as described by the equation E = hν.