The half-life of plutonium-241 is approximately 13 years. a. how much of a sample weighing 2 g will remain after 70 years? b. how much time is necessary for a sample weighing 2 g to decay to 0.1 g?

A) 0.0480 grams and B) 56.16 years.

Explanation: Half live is the time in which the amount of radioactive substance remains halve of its initial amount.

The formula we use for solving this type of problem is:

where, is the initial amount and N is the remaining amount of radioactive substance and n is the number of half lives.

where, T is the time and is half life.

A) from given data, = 2 g

T = 70 years

= 13 years

N= ?

n = 5.38

N = 0.0480 g

So, 0.0480 grams of the substance will be remaining after 70 years.

B) = 2 g

N = 0.1 g

T = ?

Let's first calculate the value of n for this.

Taking log to both sides:

n = 4.32

Half life is 13 years, so we can calculate the time as:

T = 56.16 years

So, it will take 56.16 years for the radioactive substance to decay from 2 g to 0.1 g.

Explanation:

a ) 70 years = 70/13 = 5.3846 half years

fraction of matter remaining = (1/2)⁵°³⁸⁴⁶ = 0.02393

g of matter remaining = .02393 x 2 = .0479 g

b ) t = 1/λ ln 2/.1

λ is decay contant and t is time required to convert 2 g to .1 g

λ = .693 / 13 = .0533

t = 1 / .0533 ln 20

= 18.76 x 2.995 = 56.2 years.