Question

Write complete nuclear equations for the following processes: (a) tritium \(\left({ }^{3} \mathrm{H}\right)\) undergoes \(\beta\) decay, \((\mathrm{b}){ }^{242} \mathrm{Pu}\) undergoes \(\alpha\) -particle emission, (c) \({ }^{131}\) I undergoes \(\beta\) decay, (d) \({ }^{251} \mathrm{Cf}\) emits an \(\alpha\) particle.

Short answer

(a) ³H → ³He + β⁻ + ν̅ₑ (b) ²⁴²Pu → ²³⁸U + ⁴He (c) ¹³¹I → ¹³¹Xe + β⁻ + ν̅ₑ (d) ²⁵¹Cf → ²⁴⁷Cm + ⁴He

Step-by-step solution

Understand β decay

In β decay, a neutron in the nucleus converts into a proton and emits a beta particle \(\beta^-\) (an electron). The atomic number increases by 1, while the atomic mass remains unchanged.

Tritium (³H) β decay equation

Tritium has 1 proton and 2 neutrons. When it undergoes β decay, a neutron converts to a proton. This results in helium-3:\[ {}^{3}_{1}\text{H} \rightarrow {}^{3}_{2}\text{He} + \beta^- + \bar{u}_e \] where \(\bar{u}_e\) is an antineutrino.

Understand α decay

In α decay, the nucleus emits an alpha particle \(\alpha\), which consists of 2 protons and 2 neutrons (equivalent to a helium nucleus). The atomic number decreases by 2, and the atomic mass number decreases by 4.

Plutonium-242 (²⁴²Pu) α decay equation

Plutonium-242 emits an alpha particle, transforming into uranium-238:\[ {}^{242}_{94}\text{Pu} \rightarrow {}^{238}_{92}\text{U} + {}^{4}_{2}\text{He} \]

Iodine-131 (¹³¹I) β decay equation

Iodine-131 undergoes β decay, resulting in xenon-131:\[ {}^{131}_{53}\text{I} \rightarrow {}^{131}_{54}\text{Xe} + \beta^- + \bar{u}_e \]

Californium-251 (²⁵¹Cf) α decay equation

Californium-251 emits an alpha particle, becoming curium-247:\[ {}^{251}_{98}\text{Cf} \rightarrow {}^{247}_{96}\text{Cm} + {}^{4}_{2}\text{He} \]

Key concepts

Beta Decay

Beta decay is a type of radioactive decay where a neutron in an unstable atom's nucleus transforms into a proton. This process releases a beta particle, which is basically a high-speed electron also denoted by \( \beta^- \). Interestingly, this transformation also emits an antineutrino, represented as \( \bar{u}_e \). During beta decay, the atomic number of the element increases by 1 because a neutron turns into an additional proton. However, the atomic mass remains unchanged because the total number of nucleons (protons and neutrons) stays the same. Let's summarize:

• Neutron converts to a proton
• Emits a beta particle (electron)
• Releases an antineutrino
• Increases atomic number by 1
• Atomic mass remains the same

Beta decay is fascinating because it highlights the dynamic changes happening inside an atom, subtly altering its identity and properties.

Alpha Decay

In alpha decay, an unstable nucleus relieves some of its internal energy by emitting an alpha particle. An alpha particle is composed of 2 protons and 2 neutrons, which is akin to a helium nucleus. This change reduces the atomic number of the original atom by 2 and the atomic mass number by 4. As a result, the atom transforms into a new element altogether. For example, when plutonium-242 undergoes alpha decay, it becomes a different element, uranium-238. Key points about alpha decay:

• Alpha particle: 2 protons and 2 neutrons (\( {}^4_2 \text{He} \))
• Decreases atomic number by 2
• Reduces atomic mass number by 4
• Transforms the element into another element

Alpha decay signifies the impressive transformation capabilities of atoms as they strive to reach a more stable energy state.

Tritium

Tritium is a radioactive isotope of hydrogen, known as hydrogen-3 with the symbol \( {}^3 \text{H} \). Tritium contains one proton and two neutrons, making it heavier than the most common hydrogen isotope known as protium, which has no neutrons. Tritium undergoes beta decay, during which one of its neutrons transforms into a proton. This change results in tritium transforming into helium-3. Here's a breakdown:

• Symbol: \( {}^3 \text{H} \)
• 1 proton, 2 neutrons
• Undergoes beta decay \( {}^{3}_{1} ext{H} \rightarrow {}^{3}_{2} ext{He} + \beta^- + \bar{u}_e \)
• Transforms into helium-3

Tritium is quite intriguing due to its radioactive nature and potential applications like in nuclear fusion research and as a tracer in environmental studies.

Plutonium-242

Plutonium-242 is a particular isotope of plutonium, characterized by having 94 protons and 148 neutrons (total atomic mass 242). It's a synthetic element, typically produced in nuclear reactors. Plutonium-242 undergoes alpha decay, where it releases an alpha particle. This decay process transforms plutonium-242 into uranium-238. Essential aspects of plutonium-242 include:

• Symbol: \( {}^{242} \text{Pu} \)
• 94 protons, 148 neutrons
• Undergoes alpha decay \( {}^{242}_{94}\text{Pu} \rightarrow {}^{238}_{92}\text{U} + {}^{4}_{2}\text{He} \)
• Transforms to uranium-238

Plutonium-242 showcases the shift of elements into different forms through the natural process of radioactivity.

Iodine-131

Iodine-131 is a radioactive isotope of iodine that contains 53 protons and 78 neutrons. Often used in medical applications, particularly in the treatment and imaging of thyroid issues, iodine-131 undergoes beta decay. During this process, a neutron converts into a proton, resulting in the creation of xenon-131, a non-radioactive element. The details of iodine-131 include:

• Symbol: \( {}^{131} \text{I} \)
• 53 protons, 78 neutrons
• Undergoes beta decay \( {}^{131}_{53}\text{I} \rightarrow {}^{131}_{54}\text{Xe} + \beta^- + \bar{u}_e \)
• Transforms into xenon-131

The utilization of iodine-131 in medicine is a pioneering example of harnessing natural radioactive processes for beneficial human health applications.