Some watch dials are coated with a phosphor, like ZnS, and a...

Some watch dials are coated with a phosphor, like ZnS, and a polymer in which some of the $^{1} \mathrm{H}$ atoms have been replaced by $^{3} \mathrm{H}$ atoms, tritium. The phosphor emits light when struck by the beta particle from the tritium decay, causing the dials to glow in the dark. The half-life of tritium is 12.3 yr. If the light given off is assumed to be directly proportional to the amount of tritium, by how much will a dial be dimmed in a watch that is 50 yr old?

Key Concepts

Proportionality Between Activity and Observable Output

In many contexts, the observable output such as light emission or other measurable signals is directly proportional to the amount of the radioactive material present. This means that any reduction in the quantity of the radioactive substance, due to its decay, leads to a proportional reduction in the observed activity.

Beta Decay

Beta decay is a type of radioactive decay in which a beta particle (an electron or a positron) is emitted from an atomic nucleus. This process changes the composition of the nucleus and is one of the mechanisms by which unstable isotopes achieve greater stability.

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This decay occurs at a rate characteristic of the particular isotope and is described statistically by probability laws, meaning that while the decay event of any individual nucleus is random, on a large scale a predictable decay pattern emerges.

Half-Life

Half-life is the period required for half of a given quantity of a radioactive isotope to decay. It is a crucial parameter in understanding radioactive processes because it provides a measure of how long a substance remains active and is used in calculations to predict the remaining amount of a radioactive substance over time.

Exponential Decay Law

The exponential decay law by which radioactive decay is described mathematically states that the quantity of the radioactive substance decreases exponentially as a function of time. This law is expressed with the formula N = N?(1/2)^(t/T?/?), where N? is the initial quantity, t is the elapsed time, and T?/? is the half?life.

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