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?

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/t_1/2                (1)

Where t_1/2 is the halflife. 

To answer the question we need to find t. Rearranging equation (1) we have:

- t_1/2  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