Problem 20 - Chemistry The Central Science In Si Units

Question

Each of the following nuclei undergoes either beta decay or positron emission. Predict the type of emission for each: (a) \(\frac{90}{38} \mathrm{Sr},(\mathbf{b})_{38}^{85} \mathrm{Sr}\) (c) potassium-40, (d) sulfur-30.

Step-by-Step Solution

Answer

(a) Beta decay, (b) Positron emission, (c) Beta decay or positron emission, (d) Positron emission.

Step 1: Understand Beta Decay and Positron Emission

Beta decay occurs when a nucleus has an excess number of neutrons compared to protons, turning a neutron into a proton and emitting an electron (beta particle). Positron emission happens when a nucleus has an excess number of protons compared to neutrons, turning a proton into a neutron and emitting a positron.

Step 2: Analyze Strontium-90 (8^{90} ext{Sr})

Strontium-90 has 38 protons and 52 neutrons. Given the excess neutrons, it is more stable undergoing beta decay, emitting an electron and increasing the proton number by 1, forming yttrium-90 (9^{90} ext{Y}).

Step 3: Analyze Strontium-85 (8^{85} ext{Sr})

Strontium-85 has 38 protons and 47 neutrons. The neutron-to-proton ratio is closer to stability for light nuclei, and excess protons suggest beta decay is less likely. It would undergo positron emission or electron capture, common for elements where the proton count is higher than neutron count for light nuclei.

Step 4: Analyze Potassium-40 (
9^{40} ext{K})

Potassium-40 has 19 protons and 21 neutrons. It is unstable and can undergo electron capture (a form of positron emission) or beta decay because the neutron number is slightly higher but near stability for a light element. Typically, it will emit through beta decay turning into calcium or through electron capture turning into argon.

Step 5: Analyze Sulfur-30 (
6^{30} ext{S})

Sulfur-30 has 16 protons and 14 neutrons, meaning there are more protons than stable isotopes of sulfur would have. Therefore, it would undergo positron emission or electron capture to achieve stability by converting a proton to a neutron, reducing the proton count.

Key Concepts

Beta Decay

Beta decay is a fascinating process that occurs in certain unstable nuclei. Let's break it down: imagine a nucleus with too many neutrons compared to protons. In such cases, to achieve stability, one of the neutrons converts into a proton. How does this happen? Well, in the process, an electron, known as a beta particle, is emitted. This transformation results in increasing the atomic number by 1 because a neutron has effectively turned into a proton.

Essentially, beta decay helps the nucleus reach a more stable configuration by adjusting the neutron-to-proton ratio. It's more common in isotopes where there are surplus neutrons. The emitted beta particle carries away some of the excess energy, helping balance the energy in the nucleus<.br>
In nuclear reactions, particularly in beta decay, understanding the reasons behind the emission is crucial. In cases with isotopes like Strontium-90, this property is beneficial as it shifts the element toward a more stable version, in this instance, forming Yttrium-90.

Positron Emission

Positron emission is another form of decay used by unstable nuclei. Now, what's unique about it is that it's sort of the flip side of beta decay. Instead of having too many neutrons, these nuclei have excess protons, creating instability. The nucleus seeks balance by converting a proton into a neutron. During this conversion, a positron is emitted.

A positron is essentially the antimatter counterpart of an electron. Its emission decreases the atomic number by 1 while keeping the mass number constant because a proton changes into a neutron.

In situations where the proton count is notably high compared to neutrons, such as with Sulfur-30, positron emission is a likely decay path. By emitting a positron, these isotopes move closer to a more stable neutron-to-proton ratio, which is a fundamental aspect of maintaining nuclear stability.

Neutron-to-Proton Ratio

The neutron-to-proton ratio is a critical factor in determining the stability of a nucleus. At the core of nuclear stability is balancing these particles within the nucleus.

For lighter elements, a 1:1 ratio is often seen in stable nuclei. As elements become heavier, a higher proportion of neutrons is needed to balance the repulsive forces between protons.

A nucleus with too many neutrons will likely undergo beta decay to reduce its neutron count. Conversely, a surplus of protons leads to positron emission or electron capture, decreasing the proton count.

• For Strontium-90, having 52 neutrons to 38 protons directs it towards beta decay.
• On the other hand, Potassium-40 and Sulfur-30 require either positron emission or electron capture due to their neutron-to-proton ratios.

Mastering the neutron-to-proton ratio allows us to predict which decay mode an unstable nucleus might undergo to achieve stability.

Radioactive Decay

Radioactive decay encompasses various processes through which unstable atomic nuclei lose energy. These processes include beta decay, positron emission, and other similar transformations. The ultimate goal? To reach a more stable state.

In any radioactive decay, understanding the initial composition of the nucleus helps us predict the decay pathways. Each type of decay serves a specific purpose based on the imbalance present within the nucleus. Whether it's too many neutrons or excess protons, decay processes address the root issue to stabilize the atom.

Let's look at Potassium-40 as an example. This isotope can undergo both beta decay and electron capture, showing its ability to adapt its path toward stability based on its specific energy needs.

• Beta decay increases the proton count by flipping a neutron.
• In contrast, positron emission or electron capture reduces the proton count.

Through studying these decay processes, we gain insight into the natural adjustments occurring within atoms to maintain a stable, lower-energy state.