Radioactivity

The mark scheme wants the word nucleus: an alpha particle is a helium nucleus -- 2 protons and 2 neutrons, nucleon number 4, charge $+2$. Answering just "helium" describes a neutral atom that still has its electrons, and earns nothing. The same precision applies to beta: it is identical to an electron, with a single negative charge.

The two orders run in OPPOSITE directions, so candidates who learn one state the other by mistake. Ionising effect: $\alpha > \beta > \gamma$. Penetration: $\gamma > \beta > \alpha$. Alpha is therefore the MOST ionising and the LEAST penetrating -- stopped by paper. The reason: strong ionisation makes a radiation give up its energy quickly, so it cannot travel far.

Half-life is the time for half the nuclei (or the count rate) to decay -- not "the time to run out", and not half the elapsed time. Decay is repeated halving, so a sample never truly runs out. In a calculation, count how many half-lives fit the time and halve that many times; never scale by simple proportion. Going from 160 g to 10 g is a factor of 16, so 4 half-lives.

In nuclide notation an alpha particle is $^{4}_{2}\alpha$ -- nucleon number 4, proton number 2. Writing mass 6 (or 2) is the commonest slip, and it makes the equation fail to balance. A beta particle is $^{\;\;0}_{-1}\beta$; gamma changes neither number. Check $^{238}_{\;92}\text{U} \rightarrow\ ^{234}_{\;90}\text{Th} + {}^{4}_{2}\alpha$: $234+4=238$ and $90+2=92$.

In beta-decay a neutron becomes a proton plus an electron, and it leaves as the beta particle. So the nucleon number is UNCHANGED while the proton number goes UP by one, making a different element. Candidates lower it, or leave it alone, because the beta particle is negative. (Extended) $^{234}_{\;90}\text{Th} \rightarrow\ ^{234}_{\;91}\text{Pa} + {}^{\;\;0}_{-1}\beta$.

Both words are needed; they say different things. Spontaneous means the decay is unaffected by outside conditions -- temperature, pressure and chemical state make no difference. Random means you cannot predict which nucleus decays next, or exactly when. Giving only "random" leaves out the spontaneous idea, and vice versa; a full description needs both.

A detector placed near a source records the source AND the background together. To measure the source alone, first record the count rate with no source present, then subtract that background from every later reading. Because decay is random the count rate fluctuates, so count over a reasonable time or repeat readings rather than trusting one instantaneous value.