Q

# Solve it, - Atoms And Nuclei - JEE Main

Question is based on the following paragraph.

A nucleus of mass $\dpi{100} M\; +\; \Delta m\;$ is at rest and decays into two daughter nuclei of equal mass $\dpi{100} \frac{M}{2}$ each. Speed of light is $\dpi{100} c$ .

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)

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

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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