can disintegrate either by emitting an α-particle or by emitting a β^–-particle.

(a) Write the two equations showing the products of the decays.

(b) The probabilities of disintegration by α-and β-decays are in the ratio 7/13. The overall half-life of ²¹²Bi is one hour. If 1g of pure ²¹²Bi is taken at 12.00 noon, what will be the composition of this sample at 1 p.m. the same day?

In an agricultural experiment, a solution containing 1 mole of a radioactive material (t_1/2 = 14.3 days) was injected into the roots of a plant. The plant was allowed 70 hours to settle down and then activity was measured in its fruit. If the activity measured was 1 μCi, what per cent of activity is transmitted from the root to the fruit in steady state?

A vessel of volume 125 cm³ contains tritium (³H, t_1/2 = 12.3 y) at 500 kPa and 300 K. Calculate the activity of the gas.

A sample contains a mixture of ¹¹⁰Ag and ¹⁰⁸Ag isotopes each having an activity of 8.0 × 10⁸ disintegrations per second. ¹⁰⁸Ag is known to have larger half-life than ¹¹⁰Ag. The activity A is measured as a function of time and the following data are obtained.

(a) Plot ln(A/A₀) versus time.

(b) See that for large values of time, the plot is nearly linear. Deduce the half-life of ¹⁰⁸Ag from this portion of the plot.

(c) Use the half-life of ¹⁰⁸Ag to calculate the activity corresponding to ¹¹⁰Ag in the first 50 s.

(d) Plot ln(A/A₀) versus time for ¹¹⁰Ag for the first 50 s.

(e) Find the half-life of ¹⁰⁸Ag.

A human body excretes (removes by waste discharge, sweating, etc.) certain materials by a law similar to radioactivity. If technetium is injected in some form in a human body, the body excretes half the amount in 24 hours. A patient is given an injection containing ⁹⁹Tc. This isotope is radioactive with a half-life of 6 hours. The activity from the body just after the injection is 6 μCi. How much time will elapse before the activity falls to 3 μCi?