Define the becquerel - Leaving Cert Physics - Question 9 - 2013

One common device used to detect ionising radiations is the GM tube, also known as a Geiger-Müller tube.

Alpha particles are the least penetrating; they can be stopped by a sheet of paper. Beta particles have greater penetrating ability and can pass through paper but are stopped by a few millimeters of aluminum. Gamma rays are the most penetrating and can penetrate several centimeters of lead.

Alpha particles, being positively charged, are deflected in a magnetic field in one direction. Beta particles, which are negatively charged, will deflect in the opposite direction. Gamma rays, being uncharged, are not deflected in a magnetic field.

In nuclear fission, a large nucleus, such as that of uranium-235, absorbs a neutron and becomes unstable. This instability causes the nucleus to split into two smaller nuclei, releasing a significant amount of energy, along with additional neutrons that can induce further fission events, creating a chain reaction.

The beta-decay of iodine-131 can be represented as:

After 40 days, which is equivalent to 5 half-lives (since the half-life of iodine-131 is 8 days), the fraction remaining can be calculated using the formula: $N = N_0 \left(\frac{1}{2}\right)^{n}$ Where $n$ is the number of half-lives. Thus, $N = N_0 \left(\frac{1}{2}\right)^{5} = N_0 \cdot \frac{1}{32}$ This indicates that rac{1}{32} of the original amount of iodine-131 remains.

The decay constant (λ) can be calculated using the formula:

For caesium-137, with a half-life of 30 years: $λ = \frac{\ln(2)}{30 \text{ years}} = 2.31 \times 10^{-2} \text{ y}^{-1}$ To convert it to seconds: $λ = 2.31 \times 10^{-2} \text{ y}^{-1} \cdot \frac{1 ext{ year}}{3.15 \times 10^{7} \text{ seconds}} = 7.32 \times 10^{-10} \text{ s}^{-1}$

To find the number of caesium-137 atoms (N), we use the activity formula: $A = N \cdot λ$ Where A is the activity in Bq. Thus, rearranging gives:

Calculating this yields: $N = 6.83 \times 10^{12} \text{ atoms}$