Question

The barium isotope 133Ba has a half-life of 10.5 years. A sample begins with 1.1×10¹⁰ 133Ba atoms.

A.

How many are 133Ba atoms left in the sample after 5 years.  

Express your answer using two significant figures. N=_________

B.

How many are 133Ba atoms left in the sample after 30 years.

Express your answer using two significant figures. N=_________

C.

How many are 133Ba atoms left in the sample after 180 years.

Express your answer using two significant figures. N=_________

Thank you for your help!

Answer 1

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,

  

where t Issa the half life, here, t = 10.5 years

  

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

where,

K = rate constant = 0.066 years^-1

t = time taken for decay process

N₀ = initial amount of reactant = 1.1 × 10¹⁰ g

N = amount of reactant left after decay.

a) t = 5 years

Putting values in the equation, we get :

  

  = 7.9 × 10⁹ atoms

b) t = 30 years

= 1.5 × 10⁹ atoms

c) t = 180 years

  

  = 7.6 × 10⁴ atoms