A certain watch’s luminous glow is due to zinc sulfide paint that is energized by beta particles given off by tritium, the radioactive hydrogen isotope 3 H, which has a half-life of 12.3 years. This glow has about 1/10 of its initial brightness. How many years old is the watch? g

The watch is 40.9 years old.

Explanation:

To know how many years old is the watch we need to use the following equation:

  (1)

Where:

: is the brightness in a time t = (1/10)I₀

: is the initial brightness

λ: is the decay constant of tritium

The decay constant is given by:

  (2)

Where:

: is the half-life of tritium = 12.3 years

By entering equation (2) into (1)  we have:

By solving the above equation for "t" we have:

Therefore, the watch is 40.9 years old.

I hope it helps you!

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