An AM radio station broadcasts at 1010 kHz, and its FM partner broadcasts at 98.3 MHz. Calculate and compare the energy of the photons emitted by these two radio stations.

Verified step by step guidance

1. Identify the formula to calculate the energy of a photon: \( E = h \cdot f \), where \( E \) is the energy, \( h \) is Planck's constant \( 6.626 \times 10^{-34} \text{ J}\cdot\text{s} \), and \( f \) is the frequency.
2. Convert the AM frequency from kilohertz (kHz) to hertz (Hz) by multiplying by \( 10^3 \).
3. Convert the FM frequency from megahertz (MHz) to hertz (Hz) by multiplying by \( 10^6 \).
4. Substitute the AM frequency in hertz into the energy formula to calculate the energy of the AM photon.
5. Substitute the FM frequency in hertz into the energy formula to calculate the energy of the FM photon.

Key Concepts

Photon Energy

Photon energy is the energy carried by a single photon, which 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 electromagnetic wave. Higher frequencies correspond to higher energy photons, making this concept essential for comparing the energy of photons emitted by different radio stations.

Frequency and Wavelength

Frequency (ν) is the number of cycles of a wave that pass a point per second, measured in hertz (Hz). Wavelength (λ) is the distance between successive peaks of a wave, and they are inversely related: as frequency increases, wavelength decreases. Understanding this relationship is crucial for converting between frequency and energy when analyzing electromagnetic radiation.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, ranging from radio waves to gamma rays. Radio frequencies, such as those used by AM and FM stations, fall at the lower end of the spectrum. Recognizing where these frequencies lie helps in understanding their properties and the energy associated with them, which is vital for the comparison in the given question.