Lise Meitner and Marie Curie are the only women scientists to have elements named after them - Leaving Cert Physics - Question 9 - 2016

Radioactivity is defined as the spontaneous decay of an unstable nucleus, leading to the emission of radiation, including alpha, beta, or gamma radiation.

To find the energy released, we first calculate the mass defect:

• Mass before reaction: $3.966 \times 10^{-25} \text{ kg}$
• Mass after reaction: $3.967 \times 10^{-25} \text{ kg}$
• Change in mass (loss): $\Delta m = 3.966 \times 10^{-25} - 3.967 \times 10^{-25} = 2.9 \times 10^{-28} \text{ kg}$

Using Einstein's equation, $E = mc^2$ and the speed of light, $c = 3 \times 10^8 \text{ m/s}$:

$E = (2.9 \times 10^{-28})(3 \times 10^8)^2 = 2.6 \times 10^{-11} J$

On average, one neutron is required to cause a subsequent fission event, resulting in a chain reaction. Thus, this is classified as an uncontrolled reaction.

The moderator slows down the emitted neutrons, thus increasing their likelihood of causing further fission events, which is essential for maintaining a controlled chain reaction.

$^{225}_{88}Ra \rightarrow ^{221}_{87}Ac + ^{4}_{2}He$

The decay constant ( \lambda ) can be found using: ( \lambda = \frac{0.693}{t_{1/2}}) where ( t_{1/2} = 14.9 \text{ days} = 1.29 \times 10^6 ext{ s} ):

$\lambda = \frac{0.693}{1.29 \times 10^6} = 5.38 \times 10^{-7} s^{-1}$

Using the formula for activity: ( A = \lambda N ):

$5600 = (5.38 \times 10^{-7}) N \implies N \approx 1.04 \times 10^{10}$