Write nuclear equations for beta decay and radioactive decay, and discuss their effects and graphing.

A particle with mass number 0 and atomic number -1 is a beta particle (electron).
The complete nuclear equation is:

$$^{131}_{53}I \longrightarrow ^{131}_{54}Xe + \boxed{^{0}_{-1}e}$$

6. (b)
Assumption: The initial mass of $^{131}_{53}I$ is 50 grams.

$$M_t = M_0 \times \left(\frac{1}{2}\right)^n$$ $$M_t = 50 \text{ g} \times \left(\frac{1}{2}\right)^5$$ $$M_t = 50 \text{ g} \times \frac{1}{32}$$ $$M_t = \frac{50}{32} \text{ g} = \frac{25}{16} \text{ g} = 1.5625 \text{ g}$$

The mass of $^{131}_{53}I$ remaining is $\boxed{1.5625 \text{ g}}$.

6. (c)
One harmful effect of radioisotopes is increased risk of cancer.

7.
To plot a graph of the mass of iodine-131 against time, you would use the following data points:

• At time = 0 days, mass = 120 g
• At time = 8 days (1 half-life), mass = $120 \text{ g} \times \frac{1}{2} = 60 \text{ g}$
• At time = 16 days (2 half-lives), mass = $60 \text{ g} \times \frac{1}{2} = 30 \text{ g}$
• At time = 24 days (3 half-lives), mass = $30 \text{ g} \times \frac{1}{2} = 15 \text{ g}$
• At time = 32 days (4 half-lives), mass = $15 \text{ g} \times \frac{1}{2} = 7.5 \text{ g}$ Plot these points on a graph with time on the x-axis and mass on the y-axis, then draw a smooth curve connecting them.

8.
Alpha, beta, and gamma radiations can be distinguished by their behavior in an electric or magnetic field:

• Alpha ($\alpha$) particles are positively charged and are deflected towards the negative plate in an electric field. They have the largest mass and least penetrating power.
• Beta ($\beta$) particles are negatively charged and are deflected towards the positive plate in an electric field. They have a much smaller mass than alpha particles and are more penetrating.
• Gamma ($\gamma$) rays are electromagnetic radiation with no charge and no mass, so they are not deflected by electric or magnetic fields. They have the highest penetrating power.

9. (a)

• A neutron is a subatomic particle with no electric charge and a mass slightly greater than a proton.
• A proton is a subatomic particle with a positive electric charge (+1e) and a mass slightly less than a neutron.

9. (b)
A radioactive substance is a substance that undergoes spontaneous nuclear decay, emitting radiation (such as alpha, beta, or gamma particles/rays) to transform into a more stable nucleus.

9. (c)
Two dangers associated with radioactive substances in the environment are:

• Contamination of water and food sources, leading to internal exposure when ingested.
• Damage to living organisms and ecosystems, causing cell damage, genetic mutations, and increased risk of cancer in plants, animals, and humans.

9. (d) (i)
The nuclear equation is: $^{2}_{1}D + ^{3}_{1}T \longrightarrow ^{A}_{Z}Y + ^{1}_{0}n$
(I) Mass of Y:

$$2 + 3 = A + 1$$ $$5 = A + 1$$ $$A = 4$$

The mass of Y is $\boxed{4}$.

(II) Number of Y:

$$1 + 1 = Z + 0$$ $$2 = Z$$

The atomic number of Y is $\boxed{2}$.

9. (d) (ii)
The type of reaction undergone by the isotopes of hydrogen is nuclear fusion.

9. (e) (i)
The half-life of a radioactive substance is the time taken for half of the radioactive nuclei in a given sample to decay.

9. (e) (ii)

$$M_t = M_0 \times \left(\frac{1}{2}\right)^n$$ $$9 \text{ g} = 288 \text{ g} \times \left(\frac{1}{2}\right)^n$$ $$\frac{9}{288} = \left(\frac{1}{2}\right)^n$$ $$\frac{1}{32} = \left(\frac{1}{2}\right)^n$$

Since $2^5 = 32$, then $\left(\frac{1}{2}\right)^5 = \frac{1}{32}$.
Therefore, $n = 5$.

$$n = \frac{\text{total time}}{T_{1/2}}$$ $$5 = \frac{40 \text{ days}}{T_{1/2}}$$ $$T_{1/2} = \frac{40 \text{ days}}{5} = 8 \text{ days}$$

The half-life of the radioactive substance is $\boxed{8 \text{ days}}$.

10. (a)

A particle with mass number 4 and atomic number 2 is an alpha particle.
The complete nuclear reaction is:

$$^{226}_{88}Q \longrightarrow ^{222}_{86}P + \boxed{^{4}_{2}\alpha}$$

10. (b)
Two uses of radioisotopes in health are:

• Medical imaging for diagnosis (e.g., using technetium-99m for bone scans or iodine-131 for thyroid scans).
• Radiotherapy for cancer treatment (e.g., using cobalt-60 or iridium-192 to destroy cancerous cells).