half life

• Oct 30th 2008, 07:44 PM
amiv4
half life
An unknown radioactive element decays into non-radioactive substances. In http://webwork.math.uwyo.edu/webwork...9e71b0c211.png days the radioactivity of a sample decreases by http://webwork.math.uwyo.edu/webwork...29d20a4371.png percent.
(a) What is the half-life of the element?
• Oct 31st 2008, 03:23 AM
mr fantastic
Quote:

Originally Posted by amiv4
An unknown radioactive element decays into non-radioactive substances. In http://webwork.math.uwyo.edu/webwork...9e71b0c211.png days the radioactivity of a sample decreases by http://webwork.math.uwyo.edu/webwork...29d20a4371.png percent.
(a) What is the half-life of the element?

You have to do the same sort of thing.
• Oct 31st 2008, 05:23 PM
Shyam
Quote:

Originally Posted by amiv4
An unknown radioactive element decays into non-radioactive substances. In http://webwork.math.uwyo.edu/webwork...9e71b0c211.png days the radioactivity of a sample decreases by http://webwork.math.uwyo.edu/webwork...29d20a4371.png percent.
(a) What is the half-life of the element?

initial amount of substance, $A_0 = x$

final amount of substance, $A_N = x - 0.75x = 0.25x$

time, t = 980 days

half life = h = ?

$A_N = A_0 \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$0.25x = x \left(\frac{1}{2}\right)^{\frac{980}{h}}$

$0.25 = \left(\frac{1}{2}\right)^{\frac{980}{h}}$

$\left(\frac{1}{2}\right)^2 = \left( \frac{1}{2} \right)^{\frac{980}{h}}$

$
2 = \frac{980}{h}$

h = 490 days