Question 120S: Short Answer

1The Avogadro constant (NA = 6.02 x 1023 mol–1) is chosen to be the number of 12C atoms in a sample of that isotope with a mass of exactly 12 g. Calculate approximately the mass of an alpha particle?

What is the speed of an alpha particle if it has a kinetic energy of 1 MeV?

2210Po emits alpha particles with an energy of 5.3 MeV. The alpha particles have a range of approximately 38 mm in air at atmospheric pressure. Each alpha particle collides with air molecules in its path, causing them to ionise. The average energy to cause a molecule to ionise is 30 eV.

  1. Estimate the average number of ionisations produced per mm of path.
  2. The number of ionisations per mm increases as the alpha particle reaches the end of its range. Suggest a reason for this.

399mTc is a radioactive metal which does not occur naturally. It is widely used in medical diagnostics. It decays by a nuclear rearrangement (the superscript m means metastable) producing gamma rays. The product is the nuclide 99Tc. The photons have energy 0.142 MeV.

  1. Calculate the wavelength of the radiation.

4A solution containing a compound of the radioactive isotope 82Br is used to investigate the flow rate in an open stream of water. For safety reasons the activity of the tracer in the water samples must not exceed 10 000 Bq per litre. 82Br decays with a half-life of 35.4 h and emits gamma radiation.

  1. Calculate the maximum allowable number of atoms of 82Br in 1 litre of the stream water.
  2. Calculate the number of moles of bromine atoms present in 1 litre of stream water.

5Plutonium energy sources are used to power spacecraft travelling to the outer planets where there is insufficient solar radiation. The alpha particle source in a space probe contains 2 kg of 238Pu. The isotope has a half-life of 87 years.

  1. What is the initial activity of the source?

Protest groups fear that there is a risk that, in an accident, the probe’s radioactive fuel could be released into the atmosphere.

b.How long would it take for the activity to decline to 10% of its initial value?

c.Comment on the nature of the risk involved.

6The radioactive isotope of carbon, 14C, is used for archaeological dating. 14C emits beta particles, and has a half-life of 5730 years. This isotope is present in small amounts in the carbon present as carbon dioxide in the atmosphere, so that animals and plants also have a similar content of radioactive carbon when they are alive.

The 14C is made continually by the interaction of cosmic rays with nitrogen in the upper atmosphere. The concentration ratio between 14C and 12C stays approximately constant with time, representing an equilibrium between loss by radioactive decay and production by cosmic rays.

When an organism dies it stops exchanging carbon dioxide with the atmosphere. The 14C then decays, reducing in amount and activity year by year.

In 1991 climbers in the Alps discovered the ‘Iceman’ – a body which had been preserved in the ice of a glacier. There was evidence that he had lived in the Bronze Age. It was found that the ratio of 14C to 12C in a sample taken from his body had declined to 54% of the ratio found in the atmosphere. The half-life of 14C is 5730 years.

Use this information to estimate how long ago the Iceman lived.