Question

1 milligram radium has . Its half-life is 1620 years. How many radium atoms will disintegrate from 1 milligram of pure radium in 3240 years?

Solution

Correct option is

If the quantity of a radioactive element be N0, then the quantity left after nhalf-lives is given by 

         

The half-life of radium is 1620 years. The number of half-lives in 3240 years is 

         

The initial quantity of radium is N0 = 1 mg. Hence, the quantity ofundisintegrated radium after two half-lives is 

                 

              = 0.25 mg. 

 mass of disintegrated radium = 1 mg – 0.25 mg = 0.75 mg. 

Number of atoms in it 

              

              .

SIMILAR QUESTIONS

Q1

What is meant by the ‘half-life’ of a radioactive element? What percentage of a given mass of a radioactive substance will be left undecayed after four half-lives? 

Q2

The half-life of radon is 3.8 days. Calculate how mach radon will be left out of 1024 milligram after 38 days?

Q3

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

Q4

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.

Q5

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

Q6

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?

Q7

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.

Q8

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?

Q9

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

  

Q10

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