Americium–241, a radioactive substance, is the key component of smoke detectors, where its ionising ability is used to help detect smoke particles - Leaving Cert Physics - Question 10 - 2022

The nuclear equation for this conversion can be represented as:

$\mathrm{^{239}_{94}Pu + 2^{0}_{n} \rightarrow ^{241}_{94}Pu }$

The nuclear equation is:

$\mathrm{^{241}_{94}Pu \rightarrow ^{241}_{95}Am + e^-}$

Nuclear fission involves the splitting of a heavy nucleus into two smaller nuclei, releasing a significant amount of energy. In contrast, nuclear fusion is the process where two light nuclei combine to form a heavier nucleus, also releasing energy. Fission typically occurs in heavy elements (e.g., uranium or plutonium), while fusion occurs in light elements (e.g., hydrogen isotopes). Additionally, fission can be controlled in nuclear reactors, whereas fusion requires extremely high temperatures and pressures to occur.

The function of a moderator is to slow down fast neutrons produced during fission reactions to increase the likelihood of these neutrons being absorbed by fissile material, thus sustaining the chain reaction.

An example of a moderator is water (ordinary or heavy water).

Nuclear fusion reactors are not yet viable primarily due to the extreme conditions required to sustain fusion reactions, such as incredibly high temperatures and pressures. Additionally, effective containment of the fusion reaction and extracting usable energy in a consistent and controlled manner remains a significant technical challenge.

The decay constant ( ( \lambda )) is calculated using the formula:

$\lambda = \frac{ln(2)}{t_{1/2}}$

where ( t_{1/2} ) is the half-life. Using the half-life of 432 years:

$\lambda = \frac{ln(2)}{432} = 1.60 \times 10^{-3} \text{ year}^{-1}$

The activity (A) can be calculated using:

$A = \lambda N$

where N is the number of nuclei present. First, calculate N:

$N = \frac{0.29 \times 10^{-6} \text{ g}}{(241 \times 10^{-9} \text{ g})} = 7.22 \times 10^{4} \text{ nuclei}$

Then calculate the activity:

$A = (1.60 \times 10^{-3}) \times (7.22 \times 10^{4}) = 1.15 \times 10^{4} \text{ Bq}$