If a radioactive substance decays according to the equation N = ,where N is the number of milligrams present after t days,then the half-life,in days,of the substance is given by

Question

If a radioactive substance decays according to the equation N =  ,where N is the number of milligrams present after t days,then the half-life,in days,of the substance is given by

Quizplus · Accepted Answer

The half-life formula for radioactive decay is given by:

t1/2 = ln(2)/λ

where λ is the decay constant.

From the given equation, we can write:

N = 11e^(λt)

Taking natural logarithm on both sides, we get:

ln(N) = ln(11) + λt

Rearranging, we get:

λt = ln(N) - ln(11)

Now, if we wait for a time period of t1/2, the amount of radioactive substance will be halved.

Therefore, N/2 = 11e^(λt1/2)

Taking natural logarithm on both sides and using the value of λt from the above expression, we get:

ln(N/2) = ln(11) + λt1/2

Subtracting the two equations, we get:

λt - λt1/2 = ln(N) - ln(N/2)

Simplifying, we get:

λt1/2 = ln(2)

Therefore, t1/2 = ln(2)/λ

Comparing with the given options, we can see that option B is the correct one.

If a Radioactive Substance Decays According to the Equation N