Question 7 of 8advanced🔍 AnalyzeLong Answer5 marks

The terminology of different parts of the electromagnetic spectrum is given in the text. Use the formula E = hν (for energy of a quantum of radiation: photon) and obtain the photon energy in units of eV for different parts of the electromagnetic spectrum. In what way are the different scales of photon energies that you obtain related to the sources of electromagnetic radiation?

Correct Answer

The photon energy is given by E = hν = hc/λ, where h = 6.63×106.63 \times 10⁻³⁴ J·s, c = 3×103 \times 10⁸ m/s, and 1 eV = 1.6×101.6 \times 10⁻¹⁹ J. Using E(eV) = 1240/λ(nm), the energies for different parts are:

Radio waves (> 0.1 m): Energy < 10⁻⁵ eV (approximately 10⁻¹² to 10⁻⁵ eV)

Microwaves (0.1 m to 1 mm): Energy ~ 10⁻⁵ to 10⁻³ eV

Infrared (1 mm to 700 nm): Energy ~ 10⁻³ to 1.8 eV

Visible light (700 nm to 400 nm): Energy ~ 1.8 to 3.1 eV

Ultraviolet (400 nm to 1 nm): Energy ~ 3 to 10³ eV

X-rays (1 nm to 10⁻³ nm): Energy ~ 10³ to 10⁶ eV

Gamma rays (< 10⁻³ nm): Energy > 10⁶ eV

The different scales of photon energies are directly related to their sources. The wavelength of electromagnetic waves is correlated with the characteristic size of the system that radiates. Gamma rays originate from atomic nuclei (very small size, highest energy). X-rays are emitted from heavy atoms. Visible radiation is emitted by atoms when electrons move between energy levels. Radio waves are produced by accelerating electrons in circuits and antennas. Thus, smaller sources produce higher energy (shorter wavelength) radiation, while larger sources produce lower energy (longer wavelength) radiation. The classification of electromagnetic waves is based roughly on how the waves are produced and detected.

Exercise: EXERCISES | Q: 8.9
For More Understanding

Explanation

This question requires students to apply the photon energy formula E = hν to calculate energies across the electromagnetic spectrum and understand the relationship between energy scales and radiation sources. The key insight from the textbook is that wavelength correlates with the characteristic size of the radiating system - smaller systems (nuclei) produce higher energy photons, while larger systems (circuits/antennas) produce lower energy photons.

Solution Steps

  1. Step 1: Write the formula E = hν = hc/λ, where h = 6.63×106.63 \times 10⁻³⁴ J·s, c = 3×103 \times 10⁸ m/s

  2. Step 2: Convert energy to eV using 1 eV = 1.6×101.6 \times 10⁻¹⁹ J, giving E(eV) = 1240/λ(nm)

  3. Step 3: Calculate photon energy for each region using wavelength ranges from the table

  4. Step 4: Relate energy scales to sources using the principle that wavelength correlates with characteristic size of the radiating system