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 block of ice slides down the full height from one side of a 1m high bowl and up the other side. Assuming frictionless motion and taking g as 9.81ms-2, find the speed of the block at the bottom of the bowl and the height it reaches on the the other side.
Why is potential energy negative? What does that even mean?
By considering Newton's second law and his law of gravitation, derive an expression for gravitational field strength g in terms of its mass, m, the distance from its center of mass, r, and the gravitational constant, G.
An alpha particle is accelerated with 5MeV of kinetic energy towards the nucleus of a gold atom with atomic number 79. What is the distance of closest approach that is reached by the alpha particle?