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In this lesson, we will learn how to use measurements of activity or isotope ratios to calculate the half-lives and decay constants of unstable nuclei.

Q1:

Radon-222 has a half-life of 3.823 days. If a sample of pure radon-222 has an initial mass of 0.750 g, how much time is needed for only 0.100 g of radon-222 to remain?

Q2:

Radon-222 decays by 𝛼 emission and is one of the largest sources of radiation exposure for many people.

Write a balanced equation for the decay of radon-222.

After 12.7 days, 90.0% of a sample of radon-222 has decayed. Calculate the half-life for the decay process.

Radon-222 is most hazardous if inhaled. Which properties of 𝛼 particles are responsible for this effect?

Q3:

What is the half-life of a radioactive material?

Q4:

The half-life of 2 3 9 P u is 2 4 0 0 0 years. What fraction of 2 3 9 P u present today will be present in 1 0 0 0 years, assuming no additional 2 3 9 P u is formed?

Q5:

The decay of 1.000 g of 2 2 6 R a at 1 bar and 298 K produces 1 0 . 0 − 4 mL of gaseous 2 2 2 R a over 24 hours. Calculate the half-life of 2 2 6 R a .

Q6:

After 25.0 years, a 0.5000 g sample of 1 3 3 B a contains only 0.0961 g of 1 3 3 B a . Calculate the half-life of 1 3 3 B a .

Q7:

The half-life of 9 9 T c is 6.0 hours. Calculate the rate constant for the decay of 9 9 T c .

Q8:

Technetium-99m has a half-life of 6.01 hours. How much time is needed for 85.0% of a sample of technetium-99m to decay?

Q9:

Cobalt-60 decays to nickel-60 with a half-life of 5.27 years.

Calculate the decay constant for this process.

Calculate the fraction of a sample of cobalt-60 remaining after 15.0 years.

How much time is needed for 98.0% of a sample of cobalt-60 to decay?

Q10:

A 1 . 0 0 × 1 0 − 6 g sample of 2 5 7 M d has a half-life of 5.52 hours.

Calculate the mass of 2 5 7 M d after 70.0 minutes.

Calculate the percentage of 2 5 7 M d remaining after 3.00 days.

How much time is needed for the sample mass to decrease to 1 . 0 0 × 1 0 − 7 g?

Q11:

The isotope 2 4 0 N p undergoes 𝛽 − decay with a half-life of 1.032 hours.

Which isotope is produced by the decay?

How much time is needed for 99.0% of pure 2 4 0 N p to decay?

What percentage of a sample of pure 2 4 0 N p remains after 4.30 hours?

Q12:

What is the half-life of a radioactive material in terms of the rate constant for the radioactive decay, 𝜆 ?

Q13:

Which of the following samples would have the greatest activity?

Q14:

Iodine-131 decays with a rate constant of 0.138 d^{−1}. Calculate the half-life for this decay.

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