WJEC Chemistry for AS Level Student Book: 2nd Edition (Draft)

 1.2 Basic ideas about atoms

There are three types of calculation involving half-life: ▪ Finding the time taken for the radioactivity of a sample to fall to a certain fraction of its initial value. ▪ Finding the mass of a radioactive isotope remaining after a certain length of time. ▪ Finding the half-life of a radioactive isotope. Worked examples 1. The radioactive isotope 28 Mg has a half-life of 21 hours. (a) Calculate how long it will take for the activity of the isotope to decay to 1 ⁄ 8 its original value. (b) If you started with 2.0 g of 28 Mg, calculate the mass of this isotope remaining after 84 hours. 2. The radioactive isotope cobalt-60 is used in radiotherapy. Calculate its half-life if 3.6 × 10 –5 g of cobalt-60 decay to 4.5 × 10 –6 g in 15.9 years. 21 × 3 = 63 hours (b) 84 hours = 4 half-lives 2.0g  21 →  1.0g  21 →  0.5g  21 →  0.25g  21 →  0.125g 2. 3.6 × 10 –5 → 1.8 × 10 –5 → 9.0 × 10 –6 → 4.5 × 10 –6 is 3 half-lives. Half-life is 15.9/3 = 5.3 years Consequences for living cells Radioactive emissions are potentially harmful. However, we all receive some radiation from the normal background radiation that occurs everywhere. Workers in industries where they are exposed to radiation from radioactive isotopes are carefully monitored to ensure that they do not receive more radiation than is allowed under internationally agreed limits. Ionising radiation may damage the DNA of a cell. Damage to the DNA may lead to changes in the way the cell functions, which can cause mutations and the formation of cancerous cells at lower doses or cell death at higher doses. Personal danger from ionising radiation may come from sources outside or inside the body. With a source outside the body gamma radiation is likely to be the most hazardous. However, the opposite is true for sources inside the body and if alpha particle emitting isotopes are ingested they are far more dangerous than an equivalent activity of beta emitting or gamma emitting isotopes. Beneficial uses of radioactivity Although radiation from radioisotopes is harmful to health, at the same time many beneficial uses of radioactivity have been found. Medicine ▪ Cobalt-60 in radiotherapy for the treatment of cancer. The high energy of γ -radiation is used to kill cancer cells and prevent a malignant tumour from developing. ▪ Technetium-99m is the most commonly used medical radioisotope. It is used as a tracer, normally to label a molecule which is preferentially taken up by the tissue to be studied. 1. (a) 1  21 →  1 2 21 →  1 4 21 →  1 8

Study point

The greater the half-life of a radioactive isotope the greater the concern since the radioactivity of the isotope exists for a longer time.

Knowledge check An isotope of iodine 131 I has a half-life of 8 days. Calculate how long it would take for 1.6g of 131 I to be reduced to 0.10g of 131 I. 5

Knowledge check 30 mg of bismuth–214 decays to 3.75 mg in one hour. What is the half-life of this isotope?

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Stretch & challenge Why is α radiation the most harmful if ingested but least harmful outside the body?

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