I understand the photoelectric effect and I assumed until an hour ago that to excite an electron, the photon should have energy equal to the binding energy of the initial level plus the binding energy of the final level. as I found out solving some problems, I'm wrong. the photon should have energy that is equal to the gap of the two levels. I don't understand how does this process work? let's say I have a hydrogen atom and I want to move its electron to the second energy level, how is a photon with 10.2 energy able to do that? aren't we supposed to free the electron first (give it 13.6 ev) and then give it 3.4 ev to be in the second level?
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3$\begingroup$ This is a question that can only be answered within the quantum mechanical frame. Your question is stated within the classical frame of an electron orbiting the proton, and this model is not correct for atoms. The only way one can interact with the hydrogen atom is with photons, and it is the whole atom that changes energy levels. You cannot just give any energy you like to the electron. $\endgroup$– anna vCommented Jan 8, 2022 at 16:45
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You are possibly confused with energy levels in the atom. Firstly, we can't give energy to an electron equal to its binding energy, or else, it will leave the atom entirely lest going to a higher energy level.
The energy (total) of an electron in the ground state of let's say, a hydrogen atom has $-13.6 eV$. A negative sign represents that the electron is in a bound system and we take the energy of the electron to be zero at an infinite distance from the atom's nucleus. If we give the electron, this much energy, it goes towards infinity, so, here you are possibly confused.
The energy you would require to shift electron to higher energy level can be found by rydberg equation: $$\frac{1}{\lambda}=R_HZ^2\left[\frac{1}{n_1^2}-\frac{1}{n_2^2} \right]$$, where all signs represent usual quantities.
And, energy required $E=\frac{hc}{\lambda}$
Tell me if you still have any difficulty. Hope it helps
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$\begingroup$ thanks! Just another question please. we took the mechanism of the x-ray tube. what I understand is that the ground level has higher energy than all other levels but when an electron leaves the first level and another electron gets down to fill the hole, it releases a photon. why and how? doesn't this electron have lower energy than the one in ground level? where does it get energy from? I know energy increases with n and the ground level has lower energy (more stable) but from what I also know it has the highest energy 13.6 ev in case of the hydrogen atom. how are these two ideas compatible? $\endgroup$ Commented Jan 9, 2022 at 17:33
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$\begingroup$ I'm sorry that I'm asking lots of questions but I looked everywhere and couldn't find a satisfactory answer and when I asked my professor, I got confused even more. $\endgroup$ Commented Jan 9, 2022 at 17:35
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$\begingroup$ @MahaMostafa Actually no! The ground level has less energy than other energy levels right. The energy level is not 13.6 eV as per the standard definition of electron's potential energy which is highest at 0 eV at infinity and -13.6 eV at ground level, and it's obvious that $-13.6<0$. Let's say you change this standard definition and you define the potential energy of an electron at infinity to be let's say 100 eV. Then ground level could be 1 eV, first level 3 eV, and so on. Note that the values that I defined are random, and not correct, but to just give you intuition. $\endgroup$ Commented Jan 9, 2022 at 18:43
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$\begingroup$ @MahaMostafa Don't worry, this concept gets tricky to understand but you will eventully. Feel free to ask doubts. $\endgroup$ Commented Jan 9, 2022 at 18:46
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$\begingroup$ Thanks! when I asked my professor he told me that the minus sign is a sign but the magnitude of energy is 13.6 and that's why the concept that the ground state has lower energy really bothers me. I understand everything you said. in my head if we need to release the electron, we need to give it 13.6 ev and that's why it's very hard to release the hydrogen electron from first level. am i wrong here? that's my only problem really. $\endgroup$ Commented Jan 10, 2022 at 20:51