Question

Tritium H) is an isotope of hydrogen that is sometimes used to make the hands of watches glow in the dark. The half-life of tritium is 123 years. If you start with 1 milligram of trition and wait 49 years, approximately how much of the original tritium remains? O a.6.25 Ob.3.12% O c.25 O d. 506 O e 12.5%

Answer 1

Percentage of the isotope left is 75.87 %.

Step-by-step explanation:

Initial mass of the isotope = 1 mg

Time taken by the sample, t =
`t_{(1)/(2)}=123 years`

Formula used :

`N=N_o* e^(-\lambda t)\\\\\lambda =\frac{0.693}{t_{(1)/(2)}}`

where,

`N_o` = initial mass of isotope

N = mass of the parent isotope left after the time, (t)

`t_{(1)/(2)}` = half life of the isotope

`\lambda` = rate constant

`\lambda =(0.693)/(123 year)=0.005635 year^(-1)`

`N=N_o* e^(-\lambda * t)`

Now put all the given values in this formula, we get

`N=1 mg* e^{-0.005634 year^(-1)* 49 years}`

`N=0.7587 mg`

Percentage of the isotope left:

`(N)/(N_o)* 100`

=
`(0.7587 mg)/(1 mg)* 100`

Percentage of the isotope left is 75.87 %.