Uranium -238 has a half life of 4.5 billion years. How long will it take a 2g sample of U-238 to contain just 0.4g of U-238?
Radioactive decay is a process where the nucleus of an unstable atom, such as Uranium-238 loses energy by emitting radiation.
The half life is the average time it take for half the nuclei in a sample to undergo radioactive decay.
Given an initial sample of x with mass N(0). After a time t the mass of x left in the sample N(t) is given by:
N(t) = N(0).2-t/t1/2 (1)
Where t1/2 is the halflife.
To answer the question we need to find t. Rearranging equation (1) we have:
- t1/2 log2[N(t)/N(0)] = t (2)
subbing the values from the question into (2)
-4.5x109 log2 [0.4/ 2] = 10.4 billion years
RE
Related Physics A Level answers
All answers ▸A 12V lamp, 36W is switched on for 1 hour. Find the energy supplied by the battery.
How do you combine resistors is series and parallel?
What is the difference between nuclear fusion and nuclear fission?
A boy (25kg) and a girl (20kg) are playing on a see-saw which is 4m long. If the boy sits 1m from the centre on the left side and the girl 2m from the centre on the other, which direction will the see-saw will rotate around its centre?