Question

Item5 Time Remaining 56 minutes 30 seconds00:56:30 Item 5Item 5 Time Remaining 56 minutes 30 seconds00:56:30 A pure sample of tritium, 3H, was prepared and sealed in a container for a number of years. Tritium undergoes β decay with a half-life of 12.32 years. How long has the container been sealed if analysis of the contents shows there are 5.25 mol of 3H and 6.35 mol of 3He present? Multiple Choice A. 14.1 y B. 25.6 y C. 2.34 y D. 3.38 y E. 9.77 y

Answer 1

Answer:

option A

Step-by-step explanation:

given,

sample of tritium, ³H

$t_{1/2} = 12.32 years$

contents present of ³H = 5.25 mol

content of ³He = 6.35 mol

reaction

 $^3H\rightarrow \ ^3He$

A₀ is the initial concentration

At is the concentration after time t

A₀ = 5.25 + 6.35 = 11.6 mol

At = 5.25

now,

  $k = \dfrac{0.693}{t_{1/2}}$

  $k = \dfrac{0.693}{12.32}$

           k = 0.0563 /year

$ln(\dfrac{A_o}{A_t}) = k t$

$t = \dfrac{1}{k} ln(\dfrac{A_o}{A_t})$

$t = \dfrac{1}{0.0563} ln(\dfrac{11.6}{5.25})$

t = 14.1 yr

hence, the correct answer is option A