   Chapter 2.3, Problem 59E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Radioactive Decay You are trying to determine the half-life of a new radioactive element you have isolated. You start with 1 gram, and 2 days later, you determine that it has decayed down to 0.7 grams. What is its half-life? (Round your answer to three significant digits.) [HINT: First find an exponential model, then see Example 3.]

To determine

To calculate: The half life time of a radioactive element if it has decayed down to 0.7 gram from 1 gram in 2 days.

Explanation

Given Information:

The radioactive element has decayed down to 0.7 gram from 1 gram in 2 days.

Formula used:

The expression of exponential decay model is,

Q(t)=Q0ekt

Here, Q(t) is remaining amount at time t, Q0 is initial amount of the sample, k is decay constant and t is time in year.

The relation between decay constant and half-life time is,

tdk=ln2

Here, td is half-life time.

Calculation:

Consider the expression of exponential decay model is,

Q(t)=Q0ekt

Substitute Q(t)=0.7 gram, Q0=1 gram and t=2 days in the expression Q(t)=Q0ekt,

0.7=(1)ek(2)0.7=e2k

Take natural logarithm on both side of the expression,

ln0

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