Both questionsThank you The halflife of tritium Is 124 years

Both questions...Thank you

The half-life of tritium Is 12.4 years. How long will it take for 25% of a sample of tritium to decompose? Please round the answer to the nearest tenth. 7.5 yr 5.1 yr 6.3 yr 6.9 yr 5.7yr An isotope of thorium, ^227Th, has a half-life of 18.4 days. How long will it take for 80% of the sample to decompose? Please round the answer to the nearest tenth. 60.7 days 42.7 days 51.7 days 56.2 days 47.2 days

Solution

1) decay constant = 0.693/half life = 0.693/12.4 =0.05588

So, N(t) = Noe^(-kt)

25% to decay means : N(t) = 0.75No

0.75No = No e^(-0.05588t)

ln(0.75) = -0.05588t ; t = 5.148 years

Option 2 : 5.1 yrs

2) decay constant = 0.693/half life = 0.693/18.4 = 0.0376

So, N(t) = Noe^(-kt)

80% to decay means : N(t) = 0.2No

0.2No = Noe^(-0.0376t)

t = ln0.2/-0.0376 = 42.80 days

Option 2 : 42.7 days