# half-life word question

• May 13th 2009, 09:45 AM
jepal
half-life word question
When platinum-197 undergoes a nuclear decay it becomes gold-197. The half life of platinum-197 is 20 h

a) how long would it take to turn 90% of a 1kg of platinum-197 into gold.

0.90=1(0.5)^(t/20)
0.90/1=0.5^(t/20) log of both sides
log 0.90=t/20 log0.5
(log 0.90/log0.5)*20=t
3.04 hours=t

answer in my book is 66.4 hours! what am i doing wrong! Thanks in advance!
• May 14th 2009, 02:05 AM
Hello jepal
Quote:

Originally Posted by jepal
When platinum-197 undergoes a nuclear decay it becomes gold-197. The half life of platinum-197 is 20 h

a) how long would it take to turn 90% of a 1kg of platinum-197 into gold.

0.90=1(0.5)^(t/20)
0.90/1=0.5^(t/20) log of both sides
log 0.90=t/20 log0.5
(log 0.90/log0.5)*20=t
3.04 hours=t

answer in my book is 66.4 hours! what am i doing wrong! Thanks in advance!

You've just turned 10% into gold!

Try $0.10 = 1\times 0.5^{t/20}$ instead!