What are the definitions and differences between semiconductors, intrinsic/extrinsic semiconductors, and P-type/N-type semiconductors? Also, what particles make up an atom's nucleus?

For $^{28}_{12}Mg$, the mass number $A = 28$ and the atomic number $Z = 12$.

Number of neutrons = Mass number (A) - Atomic number (Z)

There are $\boxed{16}$ neutrons in $^{28}_{12}Mg$.

(iii) If $^{28}_{12}Mg$ nucleus emits two beta particles, write a balanced decay equation.

A beta particle is an electron, represented as $^0_{-1}e$.

When two beta particles are emitted, the atomic number increases by $2 \times 1 = 2$, and the mass number remains unchanged.
Let the resulting nucleus be $^{A'}_{Z'}X'$.

Conservation of mass number: $28 = A' + 2(0) \implies A' = 28$
Conservation of atomic number: $12 = Z' + 2(-1) \implies 12 = Z' - 2 \implies Z' = 14$

The element with atomic number 14 is Silicon (Si).
The balanced decay equation is:

(iv) If initially there are 200 radioactive atoms of $^{28}_{12}Mg$, how many radioactive atoms will be left after 42 days?

Given: Initial number of atoms ($N_0$) = 200, Half-life ($T_{1/2}$) = 21 days, Total time ($t$) = 42 days.

The number of atoms remaining ($N$) after $n$ half-lives is given by $N = N_0 \left(\frac{1}{2}\right)^n$.

After 42 days, $\boxed{50}$ radioactive atoms will be left.

9. (c) (i) Sketch the tracks of alpha and beta particles in cloud chambers.

• Alpha particle tracks: These are typically thick, straight, and short lines. They are densely ionizing, causing many ionizations along a short path.
• Beta particle tracks: These are generally thin, irregular, and long lines, often appearing as zig-zag or tortuous paths. They are less ionizing and are easily deflected by collisions with gas molecules.

(ii) Name the three properties responsible for the shape of the alpha tracks.
The three properties are:

1. Large mass: Alpha particles are relatively heavy (composed of two protons and two neutrons).
2. High positive charge: They carry a charge of +2e.
3. High kinetic energy: They are emitted with significant kinetic energy. These properties lead to strong and frequent interactions with gas molecules, causing dense ionization and a short, straight path.

(iii) State one use of radioactivity.
One use of radioactivity is in carbon dating for determining the age of archaeological artifacts.