Half Life Word Problem

Question

What is the half-life (to nearest tenth of an hour) of a substance if 100g decays to 27g in 24h?

Answer 1

You can use the following formula for half-life problems:

 

A=A_0 (1/2)^{t/h}

 

Where A_0 is an initial quantity, A is the amount left after decay over t many hours...and h is the half-life.

 

Note that for t=h, we are simply curling the initial amount in half...the definition of half-life!

 

Plug in your values into the equation and try to solve for h.  Hint: use a logarithm

Answer 2

A = a₀(1/2)^t/h, where a₀ = initial amount, t = time, h = half life.

 

A = a₀(2)^-t/h

27 = 100(2)^-24/h

27/100 = 2^-24/h

0.27 = 2^-24/h

ln 0.27 = ln 2^-24/h

ln 0.27 = (-24/h) ln 2

-1.3 ≈ (-24/h) (0.69)

-1.88 ≈ -24/h

1.88 ≈ 24/h 

h ≈ 24/1.88

h ≈ 12.77

 

The half life is approximately 12.77 hours.