Question

The half-life of  is 28 years. How much is the disintegration rate of 15 mg of this isotope? The Avogadro’s number is .

Solution

Correct option is

1 gram-atom of  has a mass of 90 g and contains  atoms. Therefore, the number of atoms in 1 g of , and that in 15 mg  is 

          

            

The half-life T of  is 28 years. Therefore, its decay constant is 

       

          

          

The rate of disintegration, when N atoms are present, is given by

       .   

Substituting the above values of  and N, we get 

         

                .

SIMILAR QUESTIONS

Q1

A sample of radioactive substance has 106 radioactive nuclei. Its half-life time is 20 seconds. How many nuclei will remain after 10 seconds?

Q2

A sample contains 10–2 kg each of the two substances A and B with half-lives 4 seconds and 8 seconds respectively. Their atomic weights are in the ratio of 1 : 2. Find the amounts of A and B after an interval of 16 seconds.

Q3

The half-life of radius is 1600 years. After how many years 25% of a radium block remains undecayed?

Q4

The half-life of polonium is 140 days. In what time will 15 g of polonium be disintegrated out of its initial mass of 16 g?

Q5

The activity of a radioactive element reduces to th of its original value in 30 years. Find the half-life and the decay constant of the element.

Q6

The half-life of thorium-X is 3.64 days. After how many days will 0.1 of the mass of a sample of the substance remain undecayed?

Q7

How much of 5.00 gram of polonium will decay in one year? The half-life of polonium is 138 days.

  

Q8

The half-life of a radioactive substance is  against . Calculate the decay rate for  atoms of the substance.

Q9

The half-life of  against . Calculate the activity of 1 g sample of . Avogadro’s number is .

Q10

1 g of particles per second. Find its half-life and average life. Avogadro’s number is .