Question

If the half-life of a sample of a radioactive substance is 30 seconds, how much would be left after 60 seconds? A. one-fourth B. half C. one-eighth D. You would need to know how many atoms you are starting with.

Answer 1

`m=m_(0)*((1)/(2))^{(60)/(30)}\\\\ m=m_(0)*((1)/(2))^(2)\\\\ m=(1)/(4)m_(0)`

If the half-life of a sample of a radioactive substance is 30 seconds, how much would be left after 60 seconds? A. one-fourth

Answer 2

Answer: A. one-fourth

Step-by-step explanation:

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

`t_{(1)/(2)}=(0.693)/(k)`

`k=\frac{0.69}{t_{(1)/(2)}}=(0.693)/(30)=0.0231`

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

`t=(2.303)/(k)\log(a)/(a-x)`

where,

k = rate constant

t = age of sample = 60 sec

a = let initial amount of the reactant = 100 g

a - x = amount left after decay process =

`60=(2.303)/(0.0231)\log(100)/(a-x)`

`(100)/(a-x)=4`

`{a-x}=25`

Thus as 25 g of radioactive substance would be left after 60 seconds, which is
`(25)/(10)=(1)/(4)` of the initial amount.