As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion :

  • Option 1)

     its kinetic energy increases but potential energy and total energy decrease
     

  • Option 2)

     kinetic energy, potential energy and total energy decrease

  • Option 3)

     kinetic energy decreases, potential energy increases but total energy remains same

     

  • Option 4)

     kinetic energy and total energy decrease but potential energy increases

 

Answers (1)

As we learnt in

Energy of electron in nth orbit -

E= -\left ( \frac{me^{4}}{8\epsilon _{0}^{2}h^{2}} \right )\frac{z^{2}}{n^{2}}

 

- wherein

E\alpha \frac{z^{2}}{n^{2}} \\\frac{me^{4}}{8\epsilon_{0}^{2}h^{2}}= 13.6ev

 

 K.E.=\frac{1}{2}mv^{2}=\frac{ze^{2}}{8\pi\epsilon_{0}r}=\frac{me^{4}z^{2}}{8\epsilon_{0}^{2}n^{2}h^{2}}

P.E.=\frac{-ze^{2}}{4\pi\epsilon_{0}r}=-\frac{mz^{2}e^{4}}{8\epsilon_{0}^{2}n^{2}h^{2}}

Total energy \frac{-ze^{2}}{8\pi\epsilon_{0}r}=\frac{-mz^{2}e^{4}}{8\epsilon_{0}^{2}n^{2}h^{2}}

When electron jump from excited to ground state its K.E. increases, while P.E and Total energy decreases.

Correct answer is 1

 


Option 1)

 its kinetic energy increases but potential energy and total energy decrease
 

This is the correction option.

Option 2)

 kinetic energy, potential energy and total energy decrease

This is an incorrect option.

Option 3)

 kinetic energy decreases, potential energy increases but total energy remains same

 

This is an incorrect option.

Option 4)

 kinetic energy and total energy decrease but potential energy increases

This is an incorrect option.

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