10.3 Radioactive Decay

A radioactive nuclide has a high decay rate. What does this mean for its half-life and activity?

For the carbon dating described in this chapter, what important assumption is made about the time variation in the intensity of cosmic rays?

A sample of radioactive material is obtained from a very old rock. A plot lnA verses t yields a slope value of $− 10^{−9} \text{s}^{−1}$ (see the figure(b)). What is the half-life of this material?

The half-life of strontium-91, $_{38}^{91} \text{S} \text{r}$ is 9.70 h. Find (a) its decay constant and (b) for an initial 1.00-g sample, the activity after 15 hours.

A radioactive sample initially contains $2.40 \times 10^{− 2}$ mol of a radioactive material whose half-life is 6.00 h. How many moles of the radioactive material remain after 6.00 h? After 12.0 h? After 36.0 h?

Calculate the activity $R$, in curies of 1.00 g of $^{226} \text{R} \text{a} .$ (b) Explain why your answer is not exactly 1.00 Ci, given that the curie was originally supposed to be exactly the activity of a gram of radium.

World War II aircraft had instruments with glowing radium-painted dials. The activity of one such instrument was $1.0 \times 10^{5}$ Bq when new. (a) What mass of $^{226} \text{R} \text{a}$ was present? (b) After some years, the phosphors on the dials deteriorated chemically, but the radium did not escape. What is the activity of this instrument 57.0 years after it was made?

Armor-piercing shells with depleted uranium cores are fired by aircraft at tanks. (The high density of the uranium makes them effective.) The uranium is called depleted because it has had its $^{235} \text{U}$ removed for reactor use and is nearly pure $^{238} \text{U}$. Depleted uranium has been erroneously called nonradioactive. To demonstrate that this is wrong: (a) Calculate the activity of 60.0 g of pure $^{238} \text{U}$. (b) Calculate th…