# Kinetics of the Rate of Decay

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## Kinetics of the Rate of Decay Answer Key

1.

Which of the following equations correctly represents the change in the number of particles per unit of time?

- [math]Rate=-{∆N}/{∆t}=k/N[/math]
- [math]Rate=-{∆N}/{∆t}=kN[/math]
- [math]Rate=-{∆t}/{∆N}=k/N[/math]
- [math]Rate=-{∆t}/{∆N}=kN[/math]

2.

What is the order of the rate of decay?

- second order
- first order
- third order
- pseudo first order

3.

Which of the following equations with a natural logarithm correctly represents rate of decay?

- [math]ln(N/N_o)=kt[/math]
- [math]ln(N/N_o)=k/t[/math]
- [math]ln(N/N_o)=-k/t[/math]
- [math]ln(N/N_o)=-kt[/math]

4.

How much of a 67.00 g sample of a radioisotope will remain after 13 years, assuming that k=0.46/year?

- 0.169 g
- 2.00 g
- 16.9 g
- 170 g

5.

How much of a 120-gram sample will remain after 20 seconds, assuming that k=0.05/second?

- 40.12 g
- 0.00025 g
- 44.15 g
- None of the above

6.

What is the value of k, assuming that 68 g of a 120-gram sample remains after 20 minutes?

- 0.28/minute
- 2.84/minute
- 28.4/minute
- 0.028/minute

7.

What is the value of k, if 70 g of a 167-gram sample remains after 37 years?

- 0.0235/year
- 2.35/year
- 23.5/year
- 235/year

8.

What is the value of k, if 80 g of a 260-gram sample remains after 99 seconds?

- 119/second
- 0.119/second
- 0.0119/second
- None of the above

9.

Determine the half-life of a radioisotope, if it has a rate constant of 0.099/day. Show your work.

- ln(50/100)=-(0.099/d)([math]t_{1/2}[/math])

-0.6931=-(0.099/d)(([math]t_{1/2}[/math])

[math]t_{1/2}[/math]=7.00 days

10.

The half-life of radioisotope with a rate constant of 0.757/year is 0.915 years.

- True
- False

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