The half-life of tritium is 12.3 yr. If the TFTR fusion...

The half-life of tritium is 12.3 yr. If the TFTR fusion reactor contained 50.0 $\mathrm{m}^{3}$ of tritium at a density equal to $2.00 \times 10^{14}$ ions/cm's, how many curies of tritium were in the plasma? State how this value compares with a fission inventory (the estimated supply of fissionable material) of $4 \times 10^{10} \mathrm{Ci} .$

Key Concepts

Volume and Unit Conversions

Converting between different units, such as from ions per cubic centimeter to ions per cubic meter, is a critical step when calculating quantities in nuclear physics problems. Proper unit conversion ensures that density values and volumes are consistently applied in the calculations of total radioactive atoms and subsequent activity.

Curie

The Curie is a unit used to measure radioactivity and is defined as 3.7 × 10^10 disintegrations per second. It provides a benchmark for comparing the activity levels of different radioactive materials, such as the tritium plasma and fissionable inventories, by quantifying their decay rates.

Radioactive Decay

Radioactive decay is the process in which a nucleus loses energy by emitting radiation. This concept is fundamental in nuclear physics and helps in determining the rate at which unstable nuclei transform into other elements or isotopes, an idea that is applied when calculating the decay of tritium in a system.

Half-life

The half-life of a radioactive substance is the time required for half of the radioactive nuclei present to decay. It provides a measure of the stability of the isotope and is a critical parameter in calculating the decay constant, which in turn is used to determine the activity of the material.

Activity

Activity is defined as the number of decays per second occurring in a radioactive sample. It is calculated by multiplying the decay constant by the number of radioactive nuclei present. This concept is essential when converting the measured quantity of a radioactive material into a unit of activity, such as curies.

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