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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 information at the left. round to the nearest tenth

Verified Answer :

Answer:

The number of days is approximately 8.                    

Step-by-step 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. \(N=\frac{N_0}{2}\)

The value of k is k=0.0856.

Substitute the values in the formula,

 \(N=N_0e^{-Kt}\)

 \(\frac{N_0}{2}=N_0e^{-(0.0856)t}\)

 \(\frac{1}{2}=e^{-(0.0856)t}\)

Taking natural log both side,

 \(\ln\frac{1}{2}=\ln e^{-(0.0856)t}\)

 \(-\ln2=-(0.0856)t\ln e\)

 \(t=\frac{-\ln2}{-0.0856}\)

 \(t=8.09\)

Therefore, The number of days is approximately 8.

britanisoto4

Answer:

8.1

Step-by-step explanation:

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