Radioactivity was discovered in 1896 by Henri Becquerel - Leaving Cert Physics - Question 8 - 2020

The nuclear equation for the first decay of U-238 (which undergoes alpha decay) is:

$\frac{238}{92}U \rightarrow \frac{234}{90}Th + \frac{4}{2}He$

The nuclear equation for the final decay of U-238 (which undergoes beta decay) is:

$\frac{206}{82}Pb \rightarrow \frac{206}{83}Bi + \beta^-$

In the uranium decay series from U-238 to Pb-206:

• The total number of alpha decays is 8 (each alpha decay decreases the mass number by 4).
• The total number of beta decays is 6 (each beta decay keeps the mass number the same but changes the atomic number).

The time taken to reduce the number of nuclei by a factor of 8 is:

$t = 3 \times T_{1/2}$ Where T_{1/2} = 4.5 \times 10^9 , \text{years}, therefore:

$t = 3 \times 4.5 \times 10^9 \approx 1.35 \times 10^{10} \, \text{years}$

The activity (A) can be calculated using the formula: $A = \lambda N$ Where:

• (N = 3.2 \times 10^{10})
• (\lambda = \frac{0.693}{T_{1/2}} = \frac{0.693}{4.5 \times 10^9} \approx 1.56 \times 10^{-10} , \text{yr}^{-1}$$ Therefore:

$A \approx 1.56 \times 10^{-10} \times 3.2 \times 10^{10} \approx 5.0 \, \text{Bq}$

Isotopes are variants of a chemical element that have the same number of protons but a different number of neutrons and, hence, different mass numbers. For instance, U-238 has 92 protons and 146 neutrons, while U-235 has 92 protons and 143 neutrons.

Radon is considered dangerous because it is a colorless, odorless gas that can accumulate in buildings and is a known carcinogen. Prolonged exposure to radon increases the risk of lung cancer.

The build-up of radon in a building can be reduced through several methods:

• Ensuring proper ventilation to allow radon to escape.
• Sealing cracks in floors and walls to minimize gas entry.
• Installing radon mitigation systems that actively reduce radon levels.