Nuclear Physics

Question

A certain isotope has a half-life of 8 days. What fraction of the original sample would remain at the end of 64 days?

64/8 = 8

1/2^8 = 1/256

Is my solution correct?

Answer 1

Your answer is correct.

Let me show how to present your solution in a way that will please your teacher.

As we know, the half-life is the time it takes for half of the nuclei in a given sample to decay. The formula for it could be written in a way

N = N₀·2 ^{- t /T},

where

N - the final amount of nuclei,

N₀ - initial number of nuclei,

t = 64 days - number of days past,

T = 8 days - half-life.

We are looking for the ratio of N to N_0. From the formula we see that

N / N₀ = 2 ^{- t /T}

If we put the given values, we will get

N / N₀ = 2 ^{- 64 / 8} = 2 ^{- 8} = 1 / 2 ⁸ = 1 /256.

As you said

N / N₀ = 1 / 256