Question

Thorium- 232 decays by a 10 -step series, ultimately yielding lead-208. How many \(\alpha\) particles and how many \(\beta\) particles are emitted?

Short answer

6 alpha particles and 4 beta particles are emitted.

Step-by-step solution

Understanding Alpha and Beta Decay

In radioactive decay, an alpha (\(\alpha\)) particle is a helium nucleus, which means it consists of 2 protons and 2 neutrons. When an \(\alpha\) particle is emitted, the atomic number of the element decreases by 2, and the mass number decreases by 4. A beta (\(\beta\)) particle is an electron, which is emitted when a neutron transforms into a proton. This increases the atomic number by 1, but the mass number remains unchanged.

Determining Total Change in Mass Number

The initial isotope is Thorium-232 \( ({}^{232}_{90}Th) \) and it decays to Lead-208 \( ({}^{208}_{82}Pb) \). Calculate the change in mass number: \[ 232 - 208 = 24 \] This total change (24) in mass number results from the emission of \(\alpha\) particles.

Calculating Number of Alpha Particles

Since each \(\alpha\) particle reduces the mass number by 4, the number of \(\alpha\) particles emitted is calculated by dividing the total change in mass number by 4:\[ \frac{24}{4} = 6 \]Thus, 6 \(\alpha\) particles are emitted.

Determining Total Change in Atomic Number

Now, calculate the change in atomic number from Thorium (90 protons) to Lead (82 protons):\[ 90 - 82 = 8 \] This change in atomic number is caused by both \(\alpha\) and \(\beta\) decays.

Relating Alpha Decay to Atomic Number Change

Recall that each \(\alpha\) particle emission decreases the atomic number by 2. Since 6 \(\alpha\) particles are emitted, they decrease the atomic number by:\[ 6 \times 2 = 12 \]Thus, atomic number decreases by 12 due to \(\alpha\) particles.

Calculating Number of Beta Particles

The observed net change in atomic number is a decrease of 8, but 12 units of decrease are attributed to \(\alpha\) decay. To offset this, \(\beta\) decay must increase the atomic number by:\[ 12 - 8 = 4 \]Thus, 4 \(\beta\) particles are emitted.

Key concepts

Alpha Decay

Alpha decay is a type of radioactive decay where an unstable nucleus emits an alpha particle. An alpha particle is effectively a helium nucleus composed of 2 protons and 2 neutrons.

When alpha decay occurs, the original element (the parent) transforms into a different element (the daughter) because of the following effects:

• The atomic number of the parent element decreases by 2. This is due to the loss of 2 protons.
• The mass number decreases by 4, accounting for the 2 protons and 2 neutrons that are ejected.

This type of decay is common among heavier elements, such as Thorium-232. Over time, an element like Thorium releases several alpha particles in a decay series until it becomes more stable.

Beta Decay

Beta decay involves the transformation of a neutron into a proton, resulting in the emission of a beta particle, which is essentially an electron. This process affects the atomic number and the identity of the original element.

During beta decay:

• The atomic number increases by 1 since a neutron becomes a proton.
• The mass number usually remains unchanged because the total count of nucleons (protons + neutrons) remains the same.

This type of decay is crucial for elements that have too many neutrons relative to protons. It allows the nucleus to achieve higher stability by balancing its neutron-to-proton ratio. In nuclear decay series, beta decay often exchanges with alpha decay to shift elements down the periodic table while transitioning to a stable isotope.

Nuclear Chemistry

Nuclear chemistry is a subdivision of chemistry that deals with the reactions and properties of atomic nuclei. It encompasses both radioactive decay processes and the resulting energetics and transformation of elements.

This field explores:

• Radioactive decay types, including alpha, beta, and gamma decay.
• Nuclear fission and fusion reactions, which release large amounts of energy.
• The application of isotopes in medical, industrial, and scientific fields.

In the given exercise, the reaction of Thorium-232 decaying to Lead-208 is an example of a nuclear chemistry process where multiple decay types contribute to the transition from a radioisotope to a stable element. Such studies not only help us understand fundamental principles of matter but also play a pivotal role in energy generation and radiopharmaceutical development.

Radioactivity

Radioactivity is the spontaneous emission of particles or energy from the unstable core of an atom. This process occurs naturally in some elements, making them release energy until they transform into stable forms.

There are various types of radioactivity:

• Alpha decay: Involving the ejection of helium nuclei, as seen in Thorium-232.
• Beta decay: Emission of electrons, helpful in changing the neutron-to-proton ratio.
• Gamma decay: Emission of energy in the form of gamma rays, often following alpha or beta decay to release excess energy.

The rate of radioactivity and the kind of particles emitted define an element's half-life and decay path. Understanding these processes can help explain phenomena in geological dating and nuclear power production.