The half-life of cesium-137 is 30 years. suppose we have a 70-mg sample. (a) find the mass that remains after t years. y(t) = mg (b) how much of the sample remains after 110 years? (round your answer to two decimal places.) mg (c) after how long will only 1 mg remain? (round your answer to one decimal place.) t = yr

Answer :

(a) The mass that remains after 't' years will be,

(b) The sample remains after 110 years will be, 5.52 mg

(c) The time taken will be, 55.0 years.

Explanation :

Formula used :

       ............(1)

where,

a = amount of reactant left after n-half lives

= Initial amount of the reactant

n = number of half lives

And as we know that,

      ..........(2)

where,

t = time

= half-life

Now equating the value of 'n' from (2) to (1), we get:

      ...........(3)

(a) Now we have to calculate the mass that remains after 't' years.

As we are given that,

= 70 mg

= 30 years

Now put all the given values in formula (3), we get:

(b) Now we have top calculate the sample remains after 110 years.

As we are given that,

t = 110 years

Now put all the given values in formula (3), we get:

(c) Now we have to calculate the time when sample 1 mg remains.

As we are given that,

a = 1 mg

Now put all the given values in formula (3), we get: