Question

(a) The radioisotope 40K constitutes 0.0117% of naturally occurring potassium and has a half life of 1.28´109 years. Calculate the activity of a 1.00 kg sample of potassium chloride (KCl). You may assume that 40K is the only radioisotope present in the sample. A mole of potassium chloride has a mass of 74.55 g

Hint: You will need to calculate the number of 40K atoms in the sample.Type or paste question here

(b) The plutonium batteries in Voyager 1 had a power output of 470 W when the spacecraft was launched in 1977. After how many years following launch will the power output have dropped to 300 W?

Answer 1

This is a question from Radioactivity, of Nuclear Physics.

From the mass of potassium chloride given, isolate the mass of potassium available. Given that 0.0117% of all potassium is radioactive. Find out the number of nuclides of radioactive potassium (K-40) available in 1.00 kg of KCl. This may be noted as N.

We need to calculate the decay constant of the radioactive decay of K-40. For that, use the relation between decay constant and half life period. Given in the question, the half life is 1.28x10^19 years. Change that to seconds by multiplying 365.35x24x60x60=365.25x86400.

The decay constant is given by, Decay Constant = loge(2)/halflife.

Activity of the sample is then given by, A or R = (decay constant) x (half life period).

Detailed working is shown in the picture attached.