91Ó°ÊÓ

After 1 min, three radioactive nuclei remain from an original sample of six. Is it valid to conclude that \(t_{1 / 2}\) equals 1 min? Is this conclusion valid if the original sample contained \(6 \times 10^{12}\) nuclei and \(3 \times 10^{12}\) remain after 1 min? Explain.

What is the specific activity (in \(\mathrm{Ci} / \mathrm{g}\) ) if \(1.65 \mathrm{mg}\) of an isotope emits \(1.56 \times 10^{6} \alpha\) particles per second?

What is the specific activity (in \(\mathrm{Bq} / \mathrm{g}\) ) if \(8.58 \mu \mathrm{g}\) of an isotope emits \(7.4 \times 10^{4} \alpha\) particles per minute?

What is the specific activity (in \(\mathrm{Bq} / \mathrm{g}\) ) if \(1.07 \mathrm{~kg}\) of an isotope emits \(3.77 \times 10^{7} \beta^{-}\) particles per minute?

If \(2.8 \times 10^{-10} \%\) of the atoms of a radioactive isotope disintegrate in \(1.0 \mathrm{yr},\) what is the decay constant of the process?

If \(1.00 \times 10^{-12} \mathrm{~mol}\) of \({ }^{135} \mathrm{Cs}\) emits \(1.39 \times 10^{3} \beta^{-}\) particles in \(1.00 \mathrm{yr},\) what is the decay constant?

The isotope \({ }^{212}_{83} \mathrm{Bi}\) has a half-life of \(1.01 \mathrm{yr}\). What mass (in mg) of a 2.00-mg sample will remain after \(3.75 \times 10^{3} \mathrm{~h}\) ?

The half-life of radium- 226 is \(1.60 \times 10^{3}\) yr. How many hours will it take for a 2.50 -g sample to decay to the point where \(0.185 \mathrm{~g}\) of the isotope remains?

Plutonium-239 \(\left(t_{1 / 2}=2.41 \times 10^{4} \mathrm{yr}\right)\) represents a serious nuclear waste hazard. If seven half-lives are required to reach a tolerable level of radioactivity, how long must \({ }^{239}\) Pu be stored?

A volcanic eruption melts a large chunk of rock, and all gases are expelled. After cooling, \({ }_{18}^{40} \mathrm{Ar}\) accumulates from the ongoing decay of \({ }_{19}^{40} \mathrm{~K}\) in the rock \(\left(t_{1 / 2}=1.25 \times 10^{9} \mathrm{yr}\right) .\) When a piece of rock is analyzed, it is found to contain 1.38 mmol of \({ }^{40} \mathrm{~K}\) and \(1.14 \mathrm{mmol}\) of \({ }^{40} \mathrm{Ar}\). How long ago did the rock cool?