Question

. the isotope tritium (3h) was used as a part of the fluorescent paint on watch dials and hands during world war ii. a watch with fluorescent hands was made in august 1943. 17% or more of the original tritium is needed to read the dial in dark places. would you be able to read the watch at night this year? (for 3h, t1/2

Answer 1

No, we will not be able to read the watch made up of tritium at night this year.

The first order decay of tritium is given by

$ln\frac{A_{t} }{A_{o} } =-k.t$

Here,

k gives the rate constant

$A_{o}$ gives the initial concentration of the substance

$A_{t}$ gives the concentration of substance after time t

According to question it is given that  $t_{1/2}$  is 12.3 years

and for the first order decay the rate constant is given by

$k=\frac{ln2}{t_{1/2}}$

$k=\frac{ln 2}{12.3}$

$k=0.056$

Now, the concentration of tritium at certain time is 16% then,

$\frac{ln[0.17A_{o}] }{A_{o} } =-0.056t$

On solving we get,

$t=31.6y$

t≅32y

Time till which time can read is $1943+32=1976$

That is why time can not be read now i.e., in 2022

Learn more about first order decay

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