Question

a radioactive substance decays exponentially. a scientist begins with 110 milligrams of a radioactive substance. after 22 hours, 55 mg of the substance remains. how many milligrams will remain after 32 hours?

Answer 1

A radioactive substance will have a decay of A ≈ 31.1936 mg after 32 hours.

Radioactive decay (additionally referred to as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the manner with the aid of using which an volatile atomic nucleus loses electricity with the aid of using radiation. A fabric containing volatile nuclei is taken into consideration radioactive.

Every atom seeks to be as strong as possible. In the case of radioactive decay, instability happens whilst there's an imbalance withinside the quantity of protons and neutrons withinside the atomic nucleus. Basically, there's an excessive amount of electricity withinside the nucleus to preserve all of the nucleons together.

Initial Radioactive substance, A₂ = 110 mg Remains substance, A = 55 mg time, t = 22 hours

Here, radioactive substance decay. exponentially.

$a=a_{0}e^{at} \\\\55=110*e^{22k} \\\\\frac{55}{110} = e^{22k} \\\\ \\e^{22k} =\frac{1}{2}$

Taking lo both side, we get ln (1/2) = lne²²K

ln (1/2) = k*22

$k=\frac{ln(1/2)}{22}$

K = -0.03150669

Substance remains after 32 hours,

t=32 hr

$A=110*e^{( (-0.03150669))*32} \\A=110*e^{(-1.2602676)}$

A = 110x 0.283578131

A = 31.19359441

A ≈ 31.1936 mg

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