Question

Examples 1. Ura nium 233 has a half-life of about 70 years. If an area is contaminated with this compound, how long will it take o reach less than 5% of its original concentration? Round to the nearest number.

Answer 1

Given:
Half life = 70 years
use relation between rate constant and half life of 1st order reaction

k = (ln 2) / k
= 0.693/(half life)
= 0.693/(70)
= 9.9*10^-3 years-1
we have:
[U]o = 100 (let initial amount is 100)
[U] = 5.0 (5 % of 100 is remaining)
k = 9.9*10^-3 years-1

use integrated rate law for 1st order reaction
ln[U] = ln[U]o - k*t
ln(5) = ln(100) - 9.9*10^-3*t
1.6094 = 4.6052 - 9.9*10^-3*t
9.9*10^-3*t = 2.9957
t = 303 years
Answer: 303 years