The barium isotope 133ba has a half-life of 10.5 years. a sample begins with 1.1×1010 133ba atoms. how many are left after (a) 5 years, (b) 30 years, and (c) 190 years?

Atoms of left in

a)

b)

c)

Explanation: The given reaction is a type of radioactive decay and all the radioactive decay follows first order reactions. Hence, to calculate the rate constant, we use the formula:

To calculate how much amount of sample is left, we use the rate law expression for first order kinetics, which is:

   ....(1)

where,

k = rate constant  =

t = time taken for decay process

= initial amount of the reactant  =

N = amount left after decay process

t = 5 years

Putting values in equation 1, we get:

t = 30 years

Putting values in equation 1, we get:

t = 190 years

Putting values in equation 1, we get: