Problem 9 - College Physics

Question

Tritium is radioactive. (a) Would you expect it to (1) \(\beta^{+},(2) \beta^{-},\) or (3) alpha decay? Why? (b) Write the nuclear equation for the correct decay and identify the daughter nucleus. Is it stable?

Step-by-Step Solution

Answer

Tritium undergoes \(\beta^{-}\) decay to form stable helium-3.

Step 1: Determine the type of decay

Tritium, or hydrogen-3, is a radioactive isotope of hydrogen with one proton and two neutrons. It has a neutron-to-proton ratio greater than 1, which suggests the likelihood of beta decay (specifically, \(\beta^{-}\) decay) where a neutron is converted into a proton by emitting an electron and an antineutrino.

Step 2: Write the nuclear equation

In \(\beta^{-}\) decay, a neutron in the nucleus of tritium converts to a proton, increasing the atomic number by 1 while the mass number remains the same. The nuclear equation for tritium decay is: \[ ^3_1\text{H} \rightarrow ^3_2\text{He} + \beta^{-} + \bar{u}_e \] where \(^3_2\text{He}\) is the daughter nucleus, \(\beta^{-}\) is the emitted electron, and \(\bar{u}_e\) is the antineutrino.

Step 3: Identify and assess the stability of the daughter nucleus

The daughter nucleus in the decay process is \(^3_2\text{He}\), which is helium-3. Helium-3 is a stable isotope of helium as it is not radioactive and does not undergo further decay under normal conditions.

Key Concepts

Radioactive Decay

Radioactive decay is a fascinating process through which an unstable atomic nucleus loses energy by emitting radiation. This process results in the transformation of the original atom (the parent) into a different atom (the daughter). It happens because some isotopes are unstable and need to reach a more stable state.
Common types of radioactive decay include:

• Alpha decay: emission of 2 protons and 2 neutrons (a helium nucleus) from the parent atom.
• Beta decay: involves the emission of beta particles (electrons or positrons).
• Gamma decay: emission of gamma rays, which are high-energy photons.

In this context, tritium (a form of hydrogen with 2 neutrons and 1 proton) undergoes beta decay. It's crucial to understand this process because it changes the identity of the element itself. In essence, radioactive decay is a natural process that helps balance atomic nuclei when they are energetically unstable.

Beta Decay

Beta decay is a type of radioactive decay that involves the transformation of a neutron into a proton, or vice versa. This is accompanied by the emission of beta particles (electrons or positrons) and neutrinos.

• In beta-minus (β⁻) decay, a neutron is transformed into a proton: an electron and an antineutrino are emitted.
• In beta-plus (β⁺) decay, a proton is transformed into a neutron: a positron and a neutrino are emitted.

For tritium, beta-minus decay is the relevant process; the neutron-rich nucleus undergoes a transformation as one of its neutrons converts into a proton. This process increases the atomic number by 1 while maintaining the mass number. As a result, the parent atom (tritium) changes into a helium atom with an additional proton, turning into helium-3.

Isotopes

Isotopes are varying forms of the same element that contain equal numbers of protons but different numbers of neutrons in their nuclei. They are an essential concept in understanding nuclear physics and chemistry. The difference in neutron number among isotopes leads to differences in mass and stability.

• Stable isotopes don't undergo radioactive decay and remain unchanged over time.
• Radioactive isotopes, however, do undergo decay and transform into different elements or isotopes.

Tritium is an example of a radioactive isotope of hydrogen. With one proton and two neutrons, it differs from the more common hydrogen isotope, protium, which contains no neutrons. This neutron-rich nature makes tritium unstable, leading to its radioactive decay through beta-minus decay. Understanding isotopes like tritium helps in learning about nuclear reactions and radioactive decay processes.

Nuclear Equations

Nuclear equations depict the changes that occur in the nucleus of an atom during a nuclear reaction, such as radioactive decay. They provide a symbolic way to express the transformation of elements and the particles involved.

• The parent nucleus is shown on the left side of the equation.
• The resulting daughter nucleus and any emitted particles are listed on the right side.

In the case of tritium decay, the nuclear equation is: \[ ^3_1\text{H} \rightarrow ^3_2\text{He} + \beta^{-} + \bar{u}_e \]Here,

• \(^3_1\text{H}\) represents tritium, the parent nucleus with one proton and two neutrons.
• \(^3_2\text{He}\) is helium-3, the stable daughter nucleus.
• \(\beta^{-}\) is the beta particle, an electron emitted during the decay process.
• \(\bar{u}_e\) is the antineutrino, a nearly massless particle also emitted in the process.

Nuclear equations are vital for understanding the identities and changes of isotopes involved in nuclear reactions.