Chapter 10: Q. 10.90 (page 1053)

The half-life of radioactive iodine is $60$ days. How much of a $50$ -mg sample will be left in $40$ days?

Short Answer

Expert verified

$31.45 m g$ of the sample will be left from $50$ mg in $40$ days.

Step by step solution

Step 1. Given information

It is given that the half-life of the element is $60$ days.

Step 2. Finding the value of k.

For an original amount, $A_{0}$ , that grows or decays at a rate, $k$ , for a certain time, $t$ , the final amount,

$A = A_{0} e^{k t}$

Then substituting the given values in the formula we get:

$A = A_{0} e^{k t} 25 = 50 e^{60 k} \frac{1}{2} = e^{60 k}$

Step 3. Use logarithmic properties

Taking logarithmic properties on both sides, we get:

$\frac{1}{2} = e^{60 k} \ln \frac{1}{2} = \ln e^{60 k} - 0.693 = 60 k [\ln e^{a} = a] k = \frac{- 0.693}{60} k = - 0.0116$

Step 4. Finding the number of decreased bacteria

Substituting the obtained value of k and the given time in the given formula, we get:

$A = A_{0} e^{k t} A = 50 e^{- 0.0116 \cdot 40} A = 50 e^{- 0.464} A = 50 \cdot 0.629 A \approx 31.45$

$31.45 m g$ of the sample will be left in $40$ days.

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The half-life of radioactive iodine is $60$ days. How much of a $50$ -mg sample will be left in $40$ days?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the value of k.

Step 3. Use logarithmic properties

Step 4. Finding the number of decreased bacteria

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The half-life of radioactive iodine is 60 days. How much of a 50-mg sample will be left in 40 days?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the value of k.

Step 3. Use logarithmic properties

Step 4. Finding the number of decreased bacteria

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Discrete Mathematics

Pure Maths

Logic and Functions

Calculus

Study anywhere. Anytime. Across all devices.

The half-life of radioactive iodine is $60$ days. How much of a $50$ -mg sample will be left in $40$ days?