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Question

An electron in a hydrogen like atom makes a transition from a state in which its de-Broglie wavelength is $\lambda_1$ to a state in which its de-Broglie wavelength is $\lambda_2$, then wavelength of photon generated due to this transition will be ___________.

The solution for this problem as given in my book is as follows:

enter image description here

In the first step, it is given that the energy difference is just equal to the kinetic energy difference. How is this possible? Why have they neglected the potential energy in calculating the energy difference since the two stationary orbits in Bohr's model have different potential as well as kinetic energies.

Please clarify my doubt.

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    $\begingroup$ There is a statement known as virial theorem. Roughly speaking, it says that in systems like this, the potential energy equals (-2)*kinetic energy. No, the potential energy is not neglected at all. $\endgroup$
    – Ivan Neretin
    Aug 15, 2019 at 5:12
  • $\begingroup$ @IvanNeretin, Thank you for your reply. I haven't heard about virial theorem, but I forgot that total energy is (-1)*kinetic energy while asking this question, which I recalled only after seeing the answer. From your comment, I learnt that the name of the property in "virial theorem". Thank you. $\endgroup$
    – Vishnu
    Aug 15, 2019 at 5:15
  • $\begingroup$ @GuruVishnu Let's talk in this room. $\endgroup$
    – William R. Ebenezer
    Aug 15, 2019 at 5:27

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enter image description here My solution... Hope this helps!!

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