Physics - Calculating Half-Life

Question

1 A radioactive source has a half-life of 80 hours. How long will it take to decay to 1/16 of its original amount?

How do you calculate this?

Answer 1

A = A₀(0.5)^t/h. where t = time, h = half life, A₀ = initial amount

0.0625A₀ = A₀(0.5)^t/80          divide both sides by A₀

0.0625 = (0.5)^t/80                 take ln of both sides

ln 0.0625 = (t/80) ln 0.5       calculate

-2.77258872 ≈ (t/80)(-0.693147181)

4 ≈ t/80

320 = t

 

After three hundred twenty hours 1/16 of the original amount remains.

 

Now the non-algebraic method.

80 hours, 1/2

160 hours, 1/4

240 hours, 1/8

320 hours, 1/16