Question 1143472
<br>
The radioactivity does not decrease.  What you mean is the amount of radioactive material decreases by 29%.<br>
(a) calculating the half life....<br>
(1) Determine the number of half lives required for the amount of radioactive material to decrease by 29% -- i.e., to decay to 71% of the original amount.<br>
{{{(1/2)^n = 0.71}}}
{{{n*log((1/2)) = log((0.71))}}}
{{{n = log((0.71))/log((1/2))}}} = 0.4941 to 4 decimal places<br>
(2) Determine the half life, given that 700 days is 0.4941 half lives.<br>
{{{half life = 700/0.4941}}} = 1416.69 days to 2 decimal places.<br>
(a) ANSWER: the half life is 1416.69 days<br>
(b) Determining the number of days for a sample of 100mg to decay to 54mg....<br>
(1) Determine the number of half lives.
{{{(1/2)^n = 0.54)}}}
{{{n*log((1/2)) = log((0.54))}}}
{{{n = log((0.54))/log((1/2))}}} = 0.889 to 3 decimal places<br>
(2) Determine the number of days in 0.889 half lives.
{{{0.889*1416.69}}} = 1259 to the nearest whole number<br>
(b) ANSWER: about 1259 days for 100mg to decay to 54mg.