10.3 Radioactive decay  (Page 4/15)

How is the initial activity rate of a radioactive substance related to its half-life?

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 ln A verses t yields a slope value of $\text{−}{10}^{\mathrm{-9}}{\text{s}}^{\mathrm{-1}}$ (see [link] (b)). What is the half-life of this material?

Show that: $\bar{T}=\frac{1}{\text{λ}}$ .

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 sample of pure carbon-14 $\left(T_{1\text{/}2}{}_{}=5730\text{y}\right)$ has an activity of $1.0\mu \text{Ci}.$ What is the mass of the sample?

A radioactive sample initially contains $2.40\times {10}^{\text{−}2}$ 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?

An old campfire is uncovered during an archaeological dig. Its charcoal is found to contain less than 1/1000 the normal amount of ${}^{14}\text{C}$ . Estimate the minimum age of the charcoal, noting that $2^{10}=1024.$

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.

Natural uranium consists of ${}^{235}\text{U}$ $(\text{percent abundance}=0.7200\text{\%}$ , $\lambda =3.12\times {10}^{\mathrm{-17}}\text{/}\text{s})$ and ${}^{238}\text{U}$ $(\text{percent abundance}=99.27\text{\%}$ , $\lambda =4.92\times {10}^{\mathrm{-18}}\text{/}\text{s}).$ What were the values for percent abundance of ${}^{235}\text{U}$ and ${}^{238}\text{U}$ when Earth formed $4.5\times {10}^9$ years ago?

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?

The ${}^{210}\text{P}\text{o}$ source used in a physics laboratory is labeled as having an activity of $1.0\text{μCi}$ on the date it was prepared. A student measures the radioactivity of this source with a Geiger counter and observes 1500 counts per minute. She notices that the source was prepared 120 days before her lab. What fraction of the decays is she observing with her apparatus?

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 the activity of 60.0 g of natural uranium, neglecting the ${}^{234}\text{U}$ and all daughter nuclides.