Uses and hazards of radiation

A radioactive isotope sitting on a hospital shelf can save a life or cause a burn depending entirely on how it is handled. The same alpha, beta and gamma rays that let doctors track a tumour, factories gauge a sheet of steel, and archaeologists date a bone can also damage living cells if the source is mishandled. Every use of radioactivity is really a bargain: harness the radiation for a specific job, then respect the clock built into the isotope — its half-life — and the precautions that keep exposure safe. This article ties the half-life idea to real applications in medicine, industry, agriculture and archaeology, then covers the hazards, natural background radiation, and the practical rules that make working with radioactive sources safe.

The core insight

A radioactive sample loses exactly half its undecayed nuclei every fixed half-life, and this predictable decay is what makes isotopes useful in medicine, industry, agriculture and dating — provided the same radiation is handled with distance, shielding and minimum exposure time to avoid its cell-damaging hazards.

The core idea

Half-life (t1/2t_{1/2}) is the time taken for half of the radioactive nuclei in a sample to decay. It is a fixed property of the isotope — cobalt-60 always has the same half-life whether you have one gram or one kilogram — and it does not depend on temperature, pressure, or chemical state. After every successive half-life, whatever mass or activity remains is halved again, so after nn whole half-lives:

Fraction remaining=(12)n\text{Fraction remaining} = \left(\frac12\right)^{n}

where: nn is the number of complete half-lives elapsed (ICSE numericals stick to whole-number nn; the exponential law N=N0e−λtN = N_0e^{-\lambda t} is not required at this level).

Uses of radioactive isotopes fall into four syllabus areas:

  • Medical. Diagnosis uses radioactive tracers — a small dose is introduced into the body and followed with a detector to check how an organ is functioning. Therapy uses controlled gamma radiation, typically from cobalt-60, aimed at cancerous cells to destroy them while sparing surrounding tissue as much as possible.
  • Industrial. Thickness gauging passes beta radiation through a moving sheet (paper, plastic, or metal foil); a detector on the far side measures how much gets through, and any change signals the sheet is too thick or too thin, letting rollers be adjusted automatically without stopping production.
  • Agricultural. Seeds are irradiated to induce useful genetic mutations for crop improvement, and tracers are used to follow how plants take up fertiliser and nutrients from soil.
  • Archaeological. Carbon dating estimates the age of once-living material by comparing the radioactive carbon remaining in a sample to the amount originally present — named and used qualitatively here, with no decay-constant calculation expected.

Hazards of radiation: ionising radiation can kill or damage living cells, cause skin burns, and alter DNA in ways that lead to mutations and a raised risk of cancer with prolonged or high-dose exposure.

Background radiation is the small, unavoidable radiation present everywhere from natural sources — cosmic rays reaching Earth from space, radioactive gases like radon seeping up from the ground, and naturally radioactive minerals in rocks and soil. It is generally low-dose and distinct from hazards caused by mishandling a radioactive source.

Safety precautions for handling radioactive sources: use long tongs, never bare hands; store sources in thick lead containers; keep the time near a source as short as possible; stay as far from the source as practical, since intensity drops off rapidly with distance; wear lead aprons and a radiation-badge dosimeter; and dispose of radioactive waste following strict, approved procedures.

Figure
A bar chart showing sample mass remaining after zero one two three and four half lives starting at eighty grams and halving each time down to five grams
Halving every half-life — 80 g sample, t half = 6 hours time elapsed mass remaining (g) 80 g 0 h, n=0 40 g 6 h, n=1 20 g 12 h, n=2 10 g 18 h, n=3 5 g 24 h, n=4
Derivation AMass remaining after whole half-lives

The goal is to derive, from the plain-language definition of half-life alone, the compact rule mass remaining=initial mass×(1/2)n\text{mass remaining} = \text{initial mass} \times (1/2)^n that turns any whole-number multiple of the half-life into the fraction of a radioactive sample still undecayed, using nothing beyond repeated halving and simple exponent bookkeeping. Step 1. Start with a sample of initial mass M0M_0 and let one half-life pass. By definition, exactly half of it has decayed, so the mass remaining is M0×12M_0 \times \frac12. Step 2. Let a second half-life pass. The rule applies again to whatever is left, not to the original amount, so the remaining mass halves once more: M0×12×12=M0×(12)2M_0 \times \frac12 \times \frac12 = M_0 \times \left(\frac12\right)^2. Step 3. Repeat this halving for every additional half-life that elapses. After nn complete half-lives, the mass remaining is M0M_0 multiplied by 12\frac12 a total of nn times, which is M0×(12)nM_0 \times \left(\frac12\right)^n. Step 4. Express the general result: mass remaining=M0(12)n\text{mass remaining} = M_0\left(\frac12\right)^n, and the mass decayed is simply M0M_0 minus this remaining mass. Since nn must be counted as a whole number of half-lives for this simple form to apply, always first divide the total elapsed time by t1/2t_{1/2} and check the result is a whole number before using the formula.

Worked example

A radioactive sample has an initial mass of 80 g and a half-life of 6 hours. Find the mass remaining after 24 hours and the mass decayed.

Step 1. Find the number of half-lives elapsed: n=24 h6 h=4n = \dfrac{24\ \text{h}}{6\ \text{h}} = 4.

Step 2. Apply the fraction-remaining formula: (12)4=116\left(\dfrac12\right)^4 = \dfrac{1}{16}.

Step 3. Compute the remaining mass: 80 g×116=5 g80\ \text{g} \times \dfrac{1}{16} = 5\ \text{g}.

Step 4. Compute the mass decayed: 80 g−5 g=75 g80\ \text{g} - 5\ \text{g} = 75\ \text{g}.

After 24 hours, 5 g of the sample remains and 75 g has decayed.

Competitive stretch

A cobalt-60 hospital source with a half-life of 5 years starts at an activity of 160 units. Step 1. Find the ratio the activity has fallen by if it now reads 20 units: 160/20=8=23160/20 = 8 = 2^3, so n=3n = 3 half-lives have passed. Step 2. Convert to years: time=n×t1/2=3×5 years=15 years\text{time} = n \times t_{1/2} = 3 \times 5\ \text{years} = 15\ \text{years}. The activity falls to 20 units after 15 years, which is why hospitals recalibrate or replace such sources well before this point.

Common traps

  • Thinking half-life is the time for the entire sample to decay — it is only for half to decay; repeated halving never mathematically reaches zero.
  • Using N=N0e−λtN = N_0e^{-\lambda t} or computing λ=0.693/t1/2\lambda = 0.693/t_{1/2} — this is outside the ICSE syllabus; always work in whole-number multiples of t1/2t_{1/2} with simple halving.
  • Mixing up background radiation (natural, always present, low-dose) with hazards from a mishandled radioactive source (avoidable, potentially high-dose).
  • Forgetting that distance is one of the simplest, most effective precautions — intensity falls off rapidly as you move away from a source, alongside shielding and minimising exposure time.

Ask the tutor: want to try another half-life numerical with a different starting mass or activity ratio — ask the AI tutor to generate a fresh practice problem.

Why does increasing distance from a radioactive source help so much if the source itself has not changed

The source still emits at the same rate, but radiation spreads outward from it, so the amount reaching any point falls quickly as you move away — a detector twice as far away receives far less than half as much. This is exactly why long tongs and simply stepping back are two of the most effective, low-cost precautions used in labs and hospitals, alongside shielding and limiting exposure time.

If half-life means half decays, does the sample ever completely disappear

No, not by this simple halving rule. Each half-life removes half of whatever remains, so the amount keeps shrinking — 1/2, then 1/4, then 1/8, and so on — but mathematically it never reaches exactly zero, only smaller and smaller fractions. In practice, after enough half-lives the remaining activity becomes so tiny it is considered negligible or safe, which is why hospitals and labs plan replacement of sources based on a manageable number of half-lives rather than waiting for "zero."

Is carbon dating something I need to calculate on my ICSE exam

No. Carbon dating is examinable only as a qualitative idea at this level — you should be able to say it compares the radioactive carbon remaining in an old sample to the amount originally present to estimate age, and name it as an archaeological use of radioactivity. You are not expected to use the decay constant or any exponential formula to calculate an actual age; that level of calculation belongs to more advanced courses.

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