Question

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 )

Solution

Correct option is

0.024 Å

The annihilation equation is  

         

   (electron)        (positron)          

The mass annihilation in this process is

       

According to energy-mass relation, the energy released is 

       

             

             

             = 1.02 MeV. 

Tow -photon are produced in this process, hence energy of each photon is

        

            

            

The wavelength corresponding to it is  

        

           

           

           = 0.024 Å.

SIMILAR QUESTIONS

Q1

A radioactivity sample contains 2.2 mg of pure  which has half-life period of 1224 seconds. Calculate the number of atoms present initially.

Q2

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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Q3

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.

   

Q4

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.    

Q5

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 .   

Q6

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 .

Q7

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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Q8

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.

Q9

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 .

Q10

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,