Radioactive plutonium-239 (t½ = 2.44 x 105 yr) is used in nuclear reactors and atomic bombs. If there are 4.4 x 102 g of the isotope in a small atomic bomb, how long will it take (in yr) for the substance to decay to 1.0 x 102 g, too small an amount for an effective bomb? This radioactive decay follows first order kinetics.

The time time taken for the sample to decay from to is

Explanation:

Expression for rate law for first order kinetics is given by:

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant

a - x = amount left after decay process  

a) for completion of half life:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

b) time taken for the sample to decay from to

The time time taken for the sample to decay from to is

when the volume of gas is   changed from   717.73 ml   to 852 ml   the temperature will   change   from 315   c to 452   c

    calculation

this is calculated using the charles law formula

that is,   v1/t1 = v2/t2

          v1=?

        t1 = 315 c   into   kelvin = 315 +273 = 588 k

        v2 = 852   ml

        t2 = 425c + 273 =698 k

make v1   the subject of the formula ( by   multiplying both side by t1)

  v1=( v2 xt1) / t2

v1= (852 ml   x 588 k)/ 698 k= 717.73 ml