A medical scientist has a 15-gram sample of I-13, And would like to know it's half-life in days. he also knows that k=0.0856 find the half-life, in days, of I-131 using the…

Question

asked Apr 12, 2018 181k views

2 Answers

Jared Nielsen · Answer 1 · 2018-04-16T10:31:26+0000

Answer:

The number of days is approximately 8.

Explanation:

Given : A medical scientist has a 15-gram sample of I-13, And would like to know it's half-life in days. he also knows that k=0.0856.

To find : The half-life, in days, of I-131 using the information at the left?

Solution :

The decay model is given by
N=N_0e^(-Kt)

We have given that,

The substance's half-life is the time it takes for the substance to decay to half its original amount.

i.e.
N=(N_0)/(2)

The value of k is k=0.0856.

Substitute the values in the formula,

N=N_0e^(-Kt)

(N_0)/(2)=N_0e^(-(0.0856)t)

(1)/(2)=e^(-(0.0856)t)

Taking natural log both side,

$\ln(1)/(2)=\ln e^(-(0.0856)t)$

$-\ln2=-(0.0856)t\ln e$

$t=(-\ln2)/(-0.0856)$

t=8.09

Therefore, The number of days is approximately 8.