Question

Americium-241 is an \(\alpha\) -particle emitter, and the rate constant for decay is \(1.605 \times 10^{-3} \mathrm{y}^{-1}\) (a) Write an equation for the decay of \(^{241} \mathrm{Am}\) (b) Determine the half-life of \(^{241} \mathrm{Am}\)

Short answer

(a) Alpha decay: \( ^{241}_{95} Am \rightarrow ^{4}_{2} He + ^{237}_{93} Np \). (b) Half-life: 431.04 years.

Step-by-step solution

Understanding Alpha Decay

Alpha decay is a process where an atomic nucleus emits an alpha particle (which consists of 2 protons and 2 neutrons, equating to a Helium nucleus). For the isotope Americium-241 ( ^{241}_{95} Am), alpha decay changes the atomic number by 2 and the mass number by 4. Therefore, the decay product will be Neptunium (Np):\[ ^{241}_{95} Am \rightarrow ^{4}_{2} He + ^{237}_{93} Np\].

Formula for Half-Life Calculation

The half-life is the time required for half of the radioactive nuclei in a sample to decay. The formula to calculate the half-life ( t_{1/2}) using the rate constant ( k) for first-order reactions is:\[t_{1/2} = \frac{0.693}{k}\].

Substitute Rate Constant

Substitute the given rate constant ( k = 1.605 \times 10^{-3} ext{y}^{-1}) into the half-life formula:\[t_{1/2} = \frac{0.693}{1.605 \times 10^{-3} ext{y}^{-1}}\].

Calculate the Half-Life

Calculate ( t_{1/2}):\[t_{1/2} = \frac{0.693}{1.605 \times 10^{-3}} = 431.04 ext{y}\].

Key concepts

Alpha Decay

In alpha decay, a radioactive isotope releases an alpha particle, which is identical to a helium nucleus. This particle consists of 2 protons and 2 neutrons. During this process, the original atom loses these particles, resulting in a decrease in the atomic number by 2 units and the atomic mass by 4 units.

For the isotope of Americium-241, which is denoted as \( ^{241}_{95} \text{Am} \), alpha decay transforms it into an isotope of another element. In this specific decay, Americium-241 becomes Neptunium-237 as shown in the decay equation:
\[ ^{241}_{95} \text{Am} \rightarrow ^{4}_{2} \text{He} + ^{237}_{93} \text{Np} \]

As you can see, the atomic number decreases by 2 (from 95 to 93), and the mass number decreases by 4 (from 241 to 237). This means that Neptunium-237 remains as a stable transformation product, continuing the chain of changes common among heavy elements.

Half-Life Calculation

The half-life of a radioactive element is the time it takes for half of any given sample of radioactive nuclei to decay.

Understanding half-life can be crucial since it determines how long a radioactive substance remains active or hazardous.

For isotopes governed by first-order kinetics, the half-life \( (t_{1/2}) \) can be calculated using the formula:
\[ t_{1/2} = \frac{0.693}{k} \]
where \( k \) is the decay constant.

The value 0.693 is a natural logarithm of 2, a constant in these calculations because during each half-life, the amount of substance is halved. By substituting the rate constant \( k = 1.605 \times 10^{-3} \text{y}^{-1} \) for Americium-241, we get:
\[ t_{1/2} = \frac{0.693}{1.605 \times 10^{-3}} \approx 431 \text{ years}\].

Thus, Americium-241 takes approximately 431 years for half of its mass to decay, demonstrating how radiative decay can extend over long durations.

Americium-241 Decay

Americium-241 (\(^{241}_{95} \text{Am} \)) is a common radioactive isotope that decays via alpha decay. This element is particularly well-known for its use in smoke detectors. It is part of the actinide series in the periodic table and is synthetic, meaning it does not occur naturally but is manufactured in nuclear reactors.

This specific decay characteristic of Americium-241 allows it to release a measurable amount of ionizing radiation, pivotal for smoke detectors to function effectively through the ionization of air particles.

Americium-241's half-life of around 431 years signifies that it stays active long enough to be reliable in consumer and industrial applications, yet not so long that it's an indefinite risk. Its most prominent transformation product in its decay chain is Neptunium-237.

• Being informed of its decay is vital for both safety measures and scientific endeavors involving nuclear chemistry.
• As it transforms, Americium provides a classic study in fundamental nuclear processes like transmutation and decay.

The predictable nature of its alpha decay makes Americium-241 a model study case in educational settings for understanding radioactive decay processes.