Cobalt-60 is a radioactive isotope used in medicine for the...

Cobalt-60 is a radioactive isotope used in medicine for the treatment of certain cancers. It produces $\beta$ particles and $\gamma$ rays, the latter having energies of 1.173 and 1.332 MeV. (1 MeV = 1 million electron-volts and 1 $\mathrm{eV}=$ $9.6485 \times 10^{4} \mathrm{J} / \mathrm{mol} .$. What are the wavelength and frequency of a $\gamma$ -ray photon with an energy of $1.173 \mathrm{MeV} ?$

Key Concepts

Electromagnetic Radiation

This concept encompasses the study of waves that propagate through space carrying energy. Gamma rays, which are a form of electromagnetic radiation, are particularly high in energy and frequency, and their behavior is described by the fundamental properties of light, such as wavelength and frequency.

Photon Energy and Planck's Equation

A photon is a quantum of electromagnetic radiation whose energy is directly proportional to its frequency. This relationship is given by Planck's equation, E = h?, where E is the energy, h is Planck's constant, and ? (nu) is the frequency. This concept is crucial for linking the energy of a photon to its measurable properties like frequency and, indirectly, its wavelength.

Relationship Between Wavelength, Frequency, and the Speed of Light

The wavelength (?) and frequency (?) of electromagnetic radiation are related by the constant speed of light (c) through the equation c = ??. This relationship is fundamental in converting between a photon's frequency and its wavelength, illustrating the wave-particle duality of light.

Unit Conversion in Energy and Photonics

In many applications, energy values may be given in different units such as electron-volts (eV) or mega electron-volts (MeV). It is important to be able to convert these units into standard units like joules (J) for accurate calculations in photonics and nuclear physics. This concept ensures that calculations are consistent and that the fundamental relationships, like E = h?, are applied correctly.

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