# Question On Physics Half lifeWatch

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Thread starter 16 years ago
#1
Hi I need some help in answering the following question,

the half life of a radio active substance is 1000 years,. How much of the original substance is left after 2000 years 9000 years. How long will it take for the substance to decay to 1% of its original mass.

thankx
0
16 years ago
#2
(Original post by pruts)
Hi I need some help in answering the following question,

the half life of a radio active substance is 1000 years,. How much of the original substance is left after 2000 years 9000 years. How long will it take for the substance to decay to 1% of its original mass.

thankx
(i) After 1 half-life, amount left = 1/2 of original substance
So after 2 h-lives, the amount left will be 1/4

(ii) From the last part, we can see that the pattern is (1/2)^n, where 'n' is the no. of h-lives.

Therefore amount left after 9 h-lives (9000yrs) = (1/2)^9 = 1.95*10^-3

(iii) 1% of the original mass = 1/100 = 0.01
So we want to know many h-lives it will take for the substance to be reduced to 0.01. So:

(1/2)^n = 0.01

There's two different ways to progress from here, one for A-level and one for GCSE.....not sure what you're doing, so I'll write both.

A-level method
Take logs on both sides:

log [ (1/2)^n ] = log (0.01)

nlog(0.5) = log(0.01)
Therefore n = log(0.01) / log(0.5) = 6.6439 h-lives

Therefore total time = 1000*6.6439 = 6643.9 yrs

GCSE method
Just do trial and improvement until you get an answer that's just under 0.01

Hope this helps,
Michael.
0
16 years ago
#3
use the forula y=ar^n

where a is the starting amount, r is 1/2 and n the number or years in question/1000.
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