Watch dials are often painted with a compound containing tritium, which has a half-life of 12.3 years. when the tritium atom undergoes beta decay the emitted electron strikes a fluorescent pigment, which then glows. if your tritium-dial watch is giving off a certain amount of light, how many half-lives must pass until the watch gives off only one-eighth as much light?

3 half-lives

Explanation:

The decay rate of the watch light intensity is given by:

where : is the intensity of light that changes with time, : is the initial intensity of light, λ: is the decay constant and t: is the decay time

For light to be only one-eighth as much light, it means:

(1)

The half-life of the tritium decay is:

(2)

By entering equation (2) into equation (1), we can find the time that must pass until the watch gives off only one-eighth as much light:

Which correspond to the next half-lives:

So, until the watch gives off only one-eighth as much light must pass 3 half-lives.

I hope it helps you!

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