This question is about radioactivity - Edexcel - GCSE Physics - Question 3 - 2021 - Paper 1

One similarity is that both fluorine-19 and its radioactive isotopes have the same number of protons, which is 9. This is characteristic of the fluorine element.

One difference is that while fluorine-19 has 10 neutrons, a radioactive isotope such as fluorine-18 has 9 neutrons. This difference in neutron number can affect the stability of the nucleus.

The new count is greater than 268 because removing the aluminium sheet increases the amount of beta radiation reaching the Geiger-Muller tube. Without the sheet, there is less absorption of beta particles, allowing for a higher detection rate.

There would be no reading on the counter because the beta source has been removed, thus there are no beta particles emitted to be detected by the Geiger-Muller tube.

The SI unit for the activity of a radioactive source is the becquerel (Bq), which is defined as one decay per second.

After 33 days, which is 3 half-lives of radium-223, the remaining number of nuclei can be calculated using the formula:

$N = N_0 \left(\frac{1}{2}\right)^n$

where $N_0 = 1.7 \times 10^{23}$, and $n = 3$. Thus,

$N = 1.7 \times 10^{23} \left(\frac{1}{2}\right)^3 = 1.7 \times 10^{23} \times \frac{1}{8} = 2.125 \times 10^{22}$

This gives approximately 2.1 \times 10^{22} radium-223 nuclei remaining.