Question

Hydrogen-

3

is radioactive and has a half life of

12.3

years. What percentage of a sample would be left after

53.3

years?

Round your answer to

2

significant digits.

Hydrogen-

3

is radioactive and has a half life of

12.3

years. What percentage of a sample would be left after

53.3

years?

Round your answer to

2

significant digits.

Answer 1

Given:

Half life = 12.3 year

use relation between rate constant and half life of 1st order reaction

k = (ln 2) / k

= 0.693/(half life)

= 0.693/(12.3)

= 5.634*10^-2 year-1

we have:

[H]o = 100.0 M (Let initial concentration be 100)

t = 53.3 year

k = 5.634*10^-2 year-1

use integrated rate law for 1st order reaction

ln[H] = ln[H]o - k*t

ln[H] = ln(100) - 5.634*10^-2*53.3

ln[H] = 4.6052 - 5.634*10^-2*53.3

ln[H] = 1.6022

[H] = e^(1.6022)

[H] = 4.96 M

4.96 M of 100 M remains which is 4.96 %

Answer: 5.0 %