A radioactive element has a half-life of h years. In 500,000 years a given amount of this element would decay to 10% of its original amount. What is the half-life of this element? Thanks for help.
Use N/N0 = e^-(ln2*t/h)
0.1 = e^-(ln2*500000/h)
ln0.1 = -ln2*500000/h
h = -ln2*500000/ln0.1 ≈ 150515 years
Also, by this simple method:
0.1 = 2^-(500,000/h)
1/10 = 2^-(500,000/h) take the reciprocal of both sides,
10 = 2^(500,000/h) take the log of both sides
500,000/h =log(10) / log(2)
h =500,000 / 3.321928
h ~ 150,515 years - the half-life of this element.