The nucleus ^198 Hg has excited states at 0.412 and 1.088...

The nucleus ${ }^{198} \mathrm{Hg}$ has excited states at 0.412 and 1.088 MeV. Following the beta decay of ${ }^{198}$ Au to ${ }^{198} \mathrm{Hg}$, three gamma rays are emitted. Find the energies of these three
gamma rays.

Key Concepts

Beta Decay

Beta decay is a type of radioactive decay in which a nucleus transforms one of its neutrons into a proton (or vice versa), emitting a beta particle (an electron or positron) and an antineutrino or neutrino. This process changes the element to a different one while often leaving the daughter nucleus in an excited state, which then decays to lower energy states through the emission of gamma rays.

Gamma Decay

Gamma decay involves the emission of high?energy photons (gamma rays) from a nucleus that is in an excited state. Unlike beta decay, gamma decay does not change the number of protons or neutrons in the nucleus but rather decreases its energy by transitioning between different nuclear energy levels.

Nuclear Excited States

Nuclear excited states are energy levels of a nucleus above its ground state. When a nucleus is created in an excited state, such as following beta decay, it will often undergo gamma decay to reach lower energy states or the ground state, releasing energy in the form of gamma radiation.

Nuclear Energy Level Transitions

Nuclear energy level transitions refer to the changes between quantized excitation levels within a nucleus. The energy difference between these levels is emitted as a gamma ray. When multiple energy levels are present, the de?excitation process can occur in a cascade involving several transitions with distinct gamma ray energies.

Energy Conservation in Nuclear Transitions

Energy conservation in nuclear transitions ensures that the energy released as gamma rays exactly matches the difference between the initial and final energy levels of the nucleus. In a decay cascade, the sum of the individual gamma ray energies equals the total energy difference from the highest excited state to the ground state.

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