Please help; I'm confused with half-life/compound interest problems.

1. Fermium-252 decays in 10 minutes to 76.1% of its original mass. Find the half-life of fermium-252.

2. How long do you have to wait until 15 mg of beryllium-7 have decayed to 4 mg, if the half-life of beryllium-7 is 53.12 days?

Half life means only half of matter is left, which means half is decayed/radiated. Formula for half life is t/2 = [(elapsed time)*(log2)]/[log(beginning amount/ending amount)]

t/2 = [(10)*(log2)]/[log(100/76.1)] = 25.378 minutes. t/2 = [10 * 0.301]/[log 1.314] = [3.01]/[0.1186] = 25.378
53.12 = [(T)*(log2)]/[log(15/4)], on solving we get, T = 101.29 days 53.12 = [T * 0.301]/[log 3.75] = [0.301 * T]/[0.574], T = [53.12 * 0.574]/[0.301] = [30.49]/[0.301] = 101.29

Answered by here2help | 2024-06-10

Explanation of half-life in chemistry and its importance in decay rates for radioactive isotopes. ;

Answered by utkarshsingh1281 | 2024-06-24

The half-life of fermium-252 is approximately 25.378 minutes. It will take around 101.29 days for 15 mg of beryllium-7 to decay to 4 mg. These calculations use the properties of radioactive decay and logarithmic functions.
;

Answered by here2help | 2024-12-23