Some watch dials are coated with a phosphor, like ZnS, and a polymer in which some of the ^1 H

step 1 The decay constant for this process can be given by k is equal to 0 .693 by t half. So just putt

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

Some watch dials are coated with a phosphor, like $\mathrm{ZnS},$ and $\mathrm{a}$ polymer in which some of the ${ }^{1} \mathrm{H}$ atoms have been replaced by ${ }^{3} \mathrm{H}$ atoms, tritium.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 years old?

Key Concepts

Radioactive Decay

Radioactive decay is a process by which unstable atomic nuclei lose energy by emitting radiation. This decay occurs randomly and is characterized by a constant probability per unit time that any given nucleus will decay, making the process statistically predictable over large numbers of atoms.

Half-life

The half-life is the time required for half of a sample of a radioactive substance to decay. It is a key measure of the rate of decay and is independent of the amount of substance present, allowing the calculation of the remaining ratio of material after any given period using an exponential decay formula.

Exponential Decay

Exponential decay is a mathematical model that describes the decrease in quantity of a substance over time when the rate of decay is directly proportional to the current amount present. In the context of radioactive decay, the remaining fraction of a substance can be computed using the formula N = N0 * (1/2)^(t/half-life), where N0 is the initial amount and t is the elapsed time.

Direct Proportionality

Direct proportionality is a relationship between two quantities in which a change in one quantity directly affects the other by a constant factor. In applications like the glowing watch dial, the brightness of the glow is directly proportional to the amount of radioactive tritium remaining, meaning that any reduction in tritium results in a proportional reduction in light output.

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