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What photon energy could be absorbed by a hydrogen atom that is in the n= $ 2 $ state?

Last updated date: 25th Jul 2024
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Hint: Since in the question, it is mentioned energy is absorbed so electrons must have jumped from n= $ 1 $ to n= $ 2 $ state that is lower to higher shell. Photons are nothing but a group of electronegative energy while electrons are negatively charged.

Complete answer:
There are six lines in the Hydrogen atom which represents the energy levels of the hydrogen atom for electrons.
When an electron has to move to an upper state then it absorbs energy.
When an electron jumps down to a lower state it emits energy.
Each energy level has its energy quantized, that is, electrons have a specific amount of energy neither than nor more of energy absorbed will allow it to go onto any other energy level.
In terms of electron volts each energy level is specified with energy and five of those energy’s are as follows:-
Energy level energy (in eV)
 $ -13.6 $ eV
 $ -3.4 $ eV
 $ -1.51 $ eV
 $ -0.85 $ eV
 $ -0.54 $ eV
For electron jumping from n= $ 1 $ to n= $ 2 $ state the required would be
  $ [(-3.4)-(-13.6)] $ eV = $ 10.2 $ eV
where $ 1 $ ev= $ 1.6\times {{10}^{-19}} $ joules.
There is another formula to calculate energy
And $ \Delta E=R(\dfrac{1}{n_{final}^{2}}-\dfrac{1}{n_{initial}^{2}}) $
where R is called Rydberg’s constant which is equal to $ 1.097\times {{10}^{7}}{{m}^{-1}} $ .

As you must have already known by now, if an electron goes from lower energy level to higher energy level let’s suppose $ 1 $ to $ 3 $ it will absorb energy since it takes energy for the electrons to move from lower to higher energy level.