Question

PLEASE HELP!!!!!!! IMA DESPRATE!!!!!!! A radioactive isotope decays exponentially. The time it takes for half of the amount to decay is called the isotope's half-life. If an isotope has a half-life of 16 hours and you initially have 154 mg, how much will you have left after 64 hours? Round to the nearest thousandth.

Answer 1

Since the isotope is initially 154 mg, the amount of radioactive isotope left after 64 hours is 9.625 mg

To answer the question, we need to know what radioactive decay is.

What is radoactive decay?

Radioactive decay is the spontaneous disintegration of a larger atom to a smaller one

What is half-life?

Half-life of a radioactive isotope is the time it takes for the isotope to decay to half its initial value.

Amount left after n half lives

The amount left after n half lives is N = (1/2)ⁿN₀ where N₀ = initial mass of isotope.

Given that the half-life of the isotope is 16 hours, and we desire the amount present after 64 hours.

The number of half-lives after 64 hours is n = time/half-life

= 64 h/16 h

= 4

Since we have 154 mg of isotope present, N₀ = 154 mg

Given that

• n = 4 and
• N₀ = 154 mg

Substituting the values of the variables into N, we have

N = (1/2)ⁿN₀

N = (1/2)⁴ × 154 mg

N = 154 mg/16

N = 9.625 mg

So, the amount of radioactive isotope left after 64 hours is 9.625 mg

Learn more about radioactive decay here:

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