The half-life of a certain radioactive element is 10 years. How much of a 20g sample
will be left after 8 years? (Hint: first find the decay constant.)

Question

The half-life of a certain radioactive element is 10 years. How much of a 20g sample
will be left after 8 years? (Hint: first find the decay constant.)

anonymous · Answer

$$    N(t) = N_0 e^{-\lambda t}. \, $$

use this, substitute the values in, and you will get the decay constant

anonymous · Answer

I already used 10 = ln(2) / k  ---> ln(2) / 10 = k.
But then what?

anonymous · Answer

Then I got A = 20e^((ln(2)/10)10). What's next? where do the 8 years come in?

anonymous · Answer

ok, the amount of radioactive element left after 8 years will be
amount remained =20/(2(8/10))
=12.5g

anonymous · Answer

in my oppinion

anonymous · Answer

where'd you get the 20 from?

anonymous · Answer

oh yea i see sorry.

anonymous · Answer

ok, what does half-life mean in the first pace? it is 10 years, meaning that after 10 years the amount will become smaler by a factor of two, that is we need to divide it by 2, but since we only wait 8 years, which is 8/10 or 0.8 of the half life,we have to multiply the half life by the ratio 0.8 to 1 so, it is 2*0.8=1.6, so after 8 years, the sample reduses by a factor of 1.6

dumbcow · Answer

Use the equation posted at the top and use t=8, k = ln(2)/10, N_0 = 20
Answer should be around 11.49 rounded