Multiple-Concept Example 7 reviews the concepts needed to...

Multiple-Concept Example 7 reviews the concepts needed to solve this problem. When uranium ${ }_{92}^{235} \mathrm{U}$ decays, it emits (among other things) a $\gamma$ ray that has a wavelength of $1.14 \times 10^{-11} \mathrm{~m}$. Determine the energy (in $\mathrm{MeV}$ ) of this $\gamma$ ray.

Key Concepts

Unit Conversion

In many physics problems, especially those in nuclear and particle physics, it is necessary to convert energy measurements from one unit to another. In this context, converting energy calculated in joules to electronvolts (specifically mega-electronvolts, MeV) is crucial since nuclear energies are typically expressed in these units.

Planck’s Constant and the Speed of Light

These are fundamental physical constants important in quantum physics. Planck’s constant (h) is a key element in the quantization of energy, while the speed of light (c) is essential for relating the frequency and wavelength of an electromagnetic wave. Together, they are used in equations that connect the properties of photons.

Photon Energy

This concept refers to the calculation of the energy carried by a photon, typically determined using the relationship E = hf, where E is the photon energy, h is Planck’s constant, and f is the frequency of the photon. By combining this with the equation f = c/?, where c is the speed of light and ? is the wavelength, one can relate the energy of a photon directly to its wavelength.

Electromagnetic Spectrum

Within the electromagnetic spectrum, gamma rays occupy the region characterized by extremely short wavelengths and very high energies. Understanding this part of the spectrum helps in recognizing that gamma radiation, such as that emitted in certain radioactive decays, involves high-energy photons.

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