Question

A 1-MeV positron collides head-on with a 1-MeV electron and they are annihilated, producing -rays. Compute total energy of the resulting -rays and their wavelength.Given : rest mass of electron or positron = 0.000549 u, 

Solution

Correct option is

The annihilation equation is 

       

   (positron)           (electron) 

The total energy of the -rays produced is equal to the sum of the rest-mass energies of the positron and the electron, plus their initial kinetic energies. Thus 

      

                  

                 

The energy is shared by the two -photon is 

      

          

           

The wavelength of the -photon is 

       

          

            

          .

SIMILAR QUESTIONS

Q1

A small quantity of solution containing  radionuclide (half-life 15 hours) of activity 1.0 microcurie is injected into the blood of a person. A sample of the blood of volume 1 cm3 taken after 5 hours show an activity of 296 disintegrations per minute. Determine the total volume of blood in the body of the person.

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Q2

The isotopes  occur in nature in the ratio 140 : 1. Assuming that at the time of earth’s formation they were present in equal ratio, make an estimation of the age of the earth. The half-lives of  respectively.

   

Q3

A radioactive isotope X has a half-life of 3 seconds. At t = 0 second, a given sample of this isotope X contains 8000 atoms. Calculate the number of decays per second in the sample at t = t1 second.    

Q4

A radioactive element of atomic weight 99 has a half-life of 6 hours. Find the activity in a solution containing 1 gram of the element in the beginning. The Avogadro’s number is .   

Q5

In an ore containing uranium, the ratio of  nuclei is 3. Calculate the age of the ore, assuming that all the lead present in the ore is the final stable product of . Take the half-life of .

Q6

The mean lives of a radioactive substance are 1620 years and 405 years for-emission and -emission respectively. Find out the time during which three-fourth of a sample will decay if it is decaying both by -emission and-emission simultaneously.

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Q7

Calculate the energy in joule equivalent to the mass of one proton. The mass of proton is 1.00728 u. Express the energy in kilowatt-hour also.

Q8

An electron-positron pair is produced by the materialization of a gamma-ray photon of 2.26 MeV. How much kinetic energy is imparted to each of the charged particle? The rest mass of elector is  and the speed of light is Take .

Q9

An electron and its antiparticle are annihilated after collision. How much energy will be obtained? What will be the wavelength of the emitted radiation (energy)? (Mass of electron , speed of light  and Planck’s constant )

Q10

A neutron breaks into a photon , an electron  and antineutrino . Calculate the energy released in this process in MeVGiven : mass of electron , mass of proton , mass of neutron .