Question

Determine the half-life of potassium if in 3460 years a 200 g sample decayed into 25 g

Answer 1

`M=m_o*(1)/(2)^(t)/(T)\\ M-mass\ aftter\ decay\\ m-initial\ mass\\ t-time\\ T-period(half-life)\\ 25=200*(1)/(2)^(3460)/(T)|:200\\ (1)/(8)=((1)/(2))^(3460)/(T)\\ ((1)/(2))^3=((1)/(2))^(3460)/(T)\\ 3=(3460)/(T)\\ T=1153(1)/(3)`

or easiest way
200g -----> 100g -------> 50g -----> 25g
We can that there were three decays.
1 decay ----------- x years
3 decays---------- 3460

`x=1153(1)/(3)`