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

Question

Some watch dials are coated with a phosphor, like ZnS, and a polymer in which some of the 1H atoms have been replaced by 3H atoms, tritium.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?

Accepted Answer

Identify the initial concept: The problem involves radioactive decay, specifically the decay of tritium (3H) with a half-life of 12.3 years.. Understand the relationship: The light emitted is directly proportional to the amount of tritium present, meaning as tritium decays, the light intensity decreases.. Use the half-life formula: The amount of a radioactive substance remaining after a certain time can be calculated using the formula: $$ N(t) = N_0 	imes (\frac{1}{2})^{\frac{t}{t_{1/2}}} $$, where $$ N(t)  is $$the remaining quantity, $$ N_0  is $$the initial quantity, $$ t  is $$the time elapsed, and $$ t_{1/2}  is $$the half-life.. Substitute the known values: Here, $$ t = 50 $$ years and $$ t_{1/2} = 12.3 $$ years. Substitute these values into the formula to find the fraction of tritium remaining after 50 years.. Calculate the dimming: The fraction of tritium remaining corresponds to the fraction of light intensity remaining. Subtract this fraction from 1 to find the fraction by which the dial has dimmed.

Verified video answer for a similar problem:

Key Concepts

Radioactive Decay and Half-Life

Proportionality in Light Emission

Exponential Decay