Samarium-146 has a half-life of 103.5 million years. after 1.035 billion years, how much samarium-146 will remain from a 205-g sample?

0.200 g
0.400 g
20.5 g
103 g

Answer : The correct option is, 0.200 g

Solution :

As we know that the radioactive decays follow first order kinetics.

First we have to calculate the rate constant of a samarium-146.

Formula used :

Putting value of in this formula, we get the rate constant.

Now we have to calculate the original amount of samarium-146.

The expression for rate law for first order kinetics is given by :

where,

k = rate constant  =

t = time taken for decay process  =

a = initial amount of the samarium-146 = 205 g

a - x = amount left after decay process  = ?

Putting values in above equation, we get the value of initial amount of samarium-146.

Therefore, the amount left of the samarium-146 is, 0.200 g

Ans: 0.200 g

Given:

Half life of Sm-146 = t1/2 = 103.5 million years

Time period, t = 1.035 billion years = 1035 million years

Original mass of sample, [A]₀ = 205 g

To determine:

Amount of sample after t = 1035 million years

Explanation:

The rate of radio active decay is given as: