Question

Q: It takes 6400 years for one gram of radium to decay away to only 1/16 (one-sixteenth) of a gram. The half-life of radium is "1600" years on my HW,
but wouldn't it be 800,
its 1/16 is 6400 years,
1/8 left is 3200 years,
1/4 left is 1600 years
and 1/2 after 800 years
but my hw is saying its 1/2 life is 1600. it seems wrong...

Answer 1

decay law is:
\[N(t)=N _{0}e ^{-t/\tau} \]
tau is half-life

Answer 2

N(t) is number of radio-isotopes at time t, N_0 is number of radioisotopes at initial time, namely t=0 sec

Answer 3

please note that, sample mass m, is equals to:
\[m=\frac{ \mu N }{ N _{A} }\]
where mu is the uranium atomic mass, and N_A is the Avogadro number.
similarly, we can write:
\[m _{0}=\frac{ \mu N _{0} }{ N _{A} }\]
inserting in the above formula, we can get:
\[m=m _{0}e ^{-t/\tau} \]

Answer 4

sorry, not uranium, but radium

Answer 5

please substitute in above formula, as follows
\[m=\frac{ m _{0} }{ 16 }\]
then solve for t

Answer 6

1=0 yrs
0.5 =1600
0.25 =3200
0.125 = 4800
0.0625 = 6400

you missed out the 4800 step

Answer 7

in fact you halved the years, not the radiation....

Answer 8

thank you, i knew i was missing something/going about it wrong