The half-life of the radioactive isotope magnesium-20 is 0.600 seconds.

How long will it take for the mass of a sample of magnesium-20 to decay from 65.6 micrograms to 8.20 micrograms?
____________seconds

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mickymike92 mickymike92 · Answer 1 · 2022-07-18T18:32:59+02:00

It will take less 1.8 seconds for the mass of a sample of magnesium-20 to decay from 65.6 micrograms to 8.20 micrograms.

The half-life of a radioactive element is the time for half the amount of a sample of the substance to decay.

After 0.6 seconds 31.25 remains

After 1.2 seconds, 15.625 remains

After 1.8 seconds, 7.9 micrograms remains.

In conclusion, it will take less 1.8 seconds for the sample to decay to 8.20 micrograms.

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pstnonsonjoku pstnonsonjoku · Answer 2 · 2022-07-18T18:33:42+02:00

The time taken for the radioactive sample to decay is 1.8 s.

The half life is the time taken for only half of the number of the radioactive isotopes to remain. Now we have;

No = 65.6 micrograms

N = 8.20 micrograms

t1/2 = 0.600 seconds

t = ?

Hence;

N/No = (1/2)^t/t1/2

8.20/ 65.6 = (1/2)^t/0.600

0.125 = (1/2)^t/0.600

1/8 = (1/2)^t/0.600

(1/2)^3 = (1/2)^t/0.600

3 = t/0.600

t = 3 * 0.600

t = 1.8 s

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