Question

Write a balanced nuclear equation for each of the following: a. Th- \(225(\alpha\) decay) b. Bi-210 ( \(\alpha\) decay) c. cesium-137 ( \(\beta\) decay) d. tin-126 ( \(\beta\) decay) e. F-18 ( \(\beta^{+}\) emission)

Short answer

a. \[ {}^{225}_{90}\text{Th} \rightarrow {}^{221}_{88}\text{Ra} + {}^{4}_{2}\text{He} \] b. \[ {}^{210}_{83}\text{Bi} \rightarrow {}^{206}_{81}\text{Tl} + {}^{4}_{2}\text{He} \] c. \[ {}^{137}_{55}\text{Cs} \rightarrow {}^{137}_{56}\text{Ba} + {}^{0}_{-1}\text{e} + \overline{u}_e \] d. \[ {}^{126}_{50}\text{Sn} \rightarrow {}^{126}_{51}\text{Sb} + {}^{0}_{-1}\text{e} + \overline{u}_e \] e. \[ {}^{18}_{9}\text{F} \rightarrow {}^{18}_{8}\text{O} + {}^{0}_{1}\text{e} + u_e \]

Step-by-step solution

Understand the type of decay

Determine which type of particle is emitted for each type of decay: \(\alpha\) decay emits a helium nucleus (\( \alpha \)), \(\beta\) decay emits an electron or a positron (depending on \( \beta^- \) or \( \beta^+ \) decay).

Write the equation for Th-225 (\(\alpha\) decay)

Thorium-225 undergoes \( \alpha \) decay. An \( \alpha \) particle has 2 protons and 2 neutrons, with a mass number of 4:\[ {}^{225}_{90}\text{Th} \rightarrow {}^{221}_{88}\text{Ra} + {}^{4}_{2}\text{He} \]

Write the equation for Bi-210 (\(\alpha\) decay)

Bismuth-210 undergoes \( \alpha \) decay:\[ {}^{210}_{83}\text{Bi} \rightarrow {}^{206}_{81}\text{Tl} + {}^{4}_{2}\text{He} \]

Write the equation for Cesium-137 (\(\beta^{-}\) decay)

Cesium-137 undergoes \( \beta^{-} \) decay, emitting an electron (\( \beta^{-} \)) and an antineutrino \( \overline{u}_e \):\[ {}^{137}_{55}\text{Cs} \rightarrow {}^{137}_{56}\text{Ba} + {}^{0}_{-1}\text{e} + \overline{u}_e \]

Write the equation for Tin-126 (\(\beta^{-}\) decay)

Tin-126 undergoes \( \beta^{-} \) decay:\[ {}^{126}_{50}\text{Sn} \rightarrow {}^{126}_{51}\text{Sb} + {}^{0}_{-1}\text{e} + \overline{u}_e \]

Write the equation for F-18 (\(\beta^{+}\) emission)

Fluorine-18 undergoes \( \beta^{+} \) emission (positron emission), emitting a positron (\( \beta^{+} \)) and a neutrino \( u_e \):\[ {}^{18}_{9}\text{F} \rightarrow {}^{18}_{8}\text{O} + {}^{0}_{1}\text{e} + u_e \]

Key concepts

Alpha Decay

Alpha decay is a type of radioactive decay where an unstable nucleus emits an alpha particle. An alpha particle consists of 2 protons and 2 neutrons, equivalent to a helium nucleus:

• It reduces the atomic number by 2.
• It reduces the mass number by 4.

For example, for Thorium-225:\[{}^{225}_{90}\text{Th} \rightarrow {}^{221}_{88}\text{Ra} + {}^{4}_{2}\text{He}\] Here, Thorium-225 decays to Radium-221 with the emission of an alpha particle.

Beta Decay

Beta decay involves the transformation of a neutron into a proton (\beta^{-} decay), or a proton into a neutron (\beta^{+} decay).

• In \beta^{-} decay, an electron (\beta^{-}) and an antineutrino (\bar{u}_e) are emitted.
• In \beta^{+} decay, a positron (\beta^{+}) and a neutrino (u_e) are emitted.

For example, Cesium-137 in \beta^{-} decay:\[{}^{137}_{55}\text{Cs} \rightarrow {}^{137}_{56}\text{Ba} + {}^{0}_{-1}\text{e} + \bar{u}_e\]In this equation, Cesium-137 decays to Barium-137 with the emission of an electron and an antineutrino.

Positron Emission

Positron emission (\beta^{+} emission) is a type of beta decay in which a proton in an unstable nucleus is converted into a neutron. During this process:

• A positron, which is the antiparticle of the electron, is emitted.
• Additionally, a neutrino is emitted.

For example, with Fluorine-18: \[{}^{18}_{9}\text{F} \rightarrow {}^{18}_{8}\text{O} + {}^{0}_{1}\text{e} + u_e\]This reaction sees Fluorine-18 decay into Oxygen-18 with the emission of a positron and a neutrino.

Nuclear Reactions

Nuclear reactions involve changes in the nucleus of an atom. They can be spontaneous, like radioactive decay, or induced by particle collisions. Key points include:

• Involvement of interactions which change the composition of the nucleus.
• Emission of particles, leading to different elements or isotopes.
• Relevance in both natural processes (e.g., radioactive decay) and man-made processes (e.g., particle accelerators).

Examples include alpha decay, beta decay, and other types of radioactive decays.

Radioactive Decay

Radioactive decay is a natural process by which an unstable atomic nucleus loses energy. This can occur via multiple paths:

• Alpha decay: Emission of alpha particles.
• Beta decay: Emission of beta particles (electrons or positrons).
• Gamma decay: Emission of gamma rays, often following alpha or beta decay.

This process helps the nucleus reach a more stable configuration. For example, Tin-126 undergoes \beta^{-} decay emitting:\[{}^{126}_{50}\text{Sn} \rightarrow {}^{126}_{51}\text{Sb} + {}^{0}_{-1}\text{e} + \bar{u}_e\]Here, Tin-126 transforms into Antimony-126, emitting an electron and an antineutrino.