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Solve it, - Atoms And Nuclei - JEE Main

Question is based on the following paragraph.

A nucleus of mass M\; +\; \Delta m\; is at rest and decays into two daughter nuclei of equal mass \frac{M}{2} each. Speed of light is c .

Question: The speed of daughter nuclei is

  • Option 1)

    c\sqrt{\frac{\Delta m}{M+\Delta m}}\; \;

  • Option 2)

    \; c{\frac{\Delta m}{M+\Delta m}}\; \;

  • Option 3)

    \; \; c\sqrt{\frac{2\Delta m}{M}}\; \;

  • Option 4)

    \; c\sqrt{\frac{\Delta m}{M}}

 
Answers (1)
142 Views

As we learnt in

energy mass equivalence -

\Delta E=\Delta m.c^{2}       

- wherein

\Delta m = mass defect

\Delta E = energy released

 

 

 Speed of each of two daughter nuclei is same. Let's say its equal to v.

Total kinetic energy is equal to energy produced in the process i.e. \Delta mc^{2}

\therefore\ \; \frac{1}{2} \left(\frac{M}{2} \right )v^{2}+\frac{1}{2} \left(\frac{M}{2} \right ) v^{2}=\Delta mc^{2}

\frac{M}{2}v^{2}=\Delta mc^{2}

\therefore \ \; v=c\sqrt{\frac{2\Delta m}{M}}

Correct option is 3.


Option 1)

c\sqrt{\frac{\Delta m}{M+\Delta m}}\; \;

This is an incorrect option.

Option 2)

\; c{\frac{\Delta m}{M+\Delta m}}\; \;

This is an incorrect option.

Option 3)

\; \; c\sqrt{\frac{2\Delta m}{M}}\; \;

This is the correct option.

Option 4)

\; c\sqrt{\frac{\Delta m}{M}}

This is an incorrect option.

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