Chapter 5: Q 9 (page 336)

Radioactive Decay
The half-life of radium is 1690 years.
If 10 grams is present now, how much will be present in 50 years?

Short Answer

Expert verified

The amount of radium present in 50 years is 9.797 grams.

Step by step solution

Step 1. Given information

The half-life of radium is 1690 years.

If 10 grams is present now, how much will be present in 50 years

Step 2. Radium present in 50 years

The amount A of radioactive material present at time t is expressed by the function $N (t) = N_{0} e^{k t}$ where $k < 0$ represents the rate of decay.

The half-life of radium is 1690 years.

Substitute $N_{0} = 10, N (t) = \frac{10}{2} = 5, t = 1690$ in the function $N (t) = N_{0} e^{k t}$

role="math" localid="1647290301897" $N (t) = N_{0} e^{k t} 5 = 10 e^{k \times 1690} \frac{1}{2} = e^{k \times 1690} \ln (0.5) = \ln (e^{k \times 1690}) \ln (0.5) = k \times 1690 k = \frac{\ln (0.5)}{1690} k = - 0.00041$

Now radium present in 50 years can be calculated by,

substituting role="math" localid="1647290364834" $N_{0} = 10, k = - 0.00041, t = 50$ in the function $N (t) = N_{0} e^{k t}$

$N (t) = N_{0} e^{k t} N (50) = 10 e^{- 0.00041 \times 50} N (50) = 9.797$

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Radioactive Decay
The half-life of radium is 1690 years.
If 10 grams is present now, how much will be present in 50 years?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Radium present in 50 years

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Radioactive DecayThe half-life of radium is 1690 years.If 10 grams is present now, how much will be present in 50 years?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Radium present in 50 years

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Pure Maths

Decision Maths

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Radioactive Decay
The half-life of radium is 1690 years.
If 10 grams is present now, how much will be present in 50 years?