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In Bohr model, we know that when an electron in Hydrogen atom goes to a lower orbital it emits some energy which is seen as spectrum.

But my question is Hydrogen has only one electron in one orbital. So how can this electron go to upper or lower orbital when there is only one orbital in Hydrogen and so how can it show any spectrum?

Theoretical
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    The hydrogen atom has in infinite number of orbitals. But it has only one electron. The electron can exist in any of those orbitals. – garyp Feb 20 '18 at 14:20
  • @garyp Is it true that H atom has infinite orbitals? – Theoretical Feb 20 '18 at 14:22
  • It is indeed true that there are an infinite number of solutions to the wave equation for hydrogen, getting asymptotically closer to being unbound. – Jon Custer Feb 20 '18 at 14:27
  • @JonCuster Can you please describe yourself in equations? – Theoretical Feb 20 '18 at 14:28
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    Yes. The energy spacing between the lower-energy states is rather large, but as the energy of the states increases, the spacing gets smaller and smaller, approaching a limit of zero when the energy of the state is zero. There are positive energy states. These are not bound. The electron will "fly away". The energies of these states form a continuum; that is, there is a state arbitrarily close in energy to any other continuum state. – garyp Feb 20 '18 at 14:29
  • @garyp Doesn't Bohr model follow Maxwell's law and end up in collision with the neucles? – Theoretical Feb 20 '18 at 14:32
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    The energy of the bound states of hydrogen can be label by $n$, the principle quantum number. The ground state has $n=1$, the next higher energy state has $n=2$ and so on. The energy of the state $n$ $E_n = -13.6 \mathrm{eV}/n^2$. For any number $n$, as large as you would like, there is a state. – garyp Feb 20 '18 at 14:34
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    Collision with nucleus: it should. This problem was one of the difficulties that physicists faced at the end of the 19th century. It pointedly demonstrated that the existing theory (Maxwell) was incomplete, and some new ideas (Quantum Mechanics) were needed. – garyp Feb 20 '18 at 14:37
  • On the collision question: https://physics.stackexchange.com/q/9415/520 https://physics.stackexchange.com/q/20003/520 – dmckee --- ex-moderator kitten Feb 20 '18 at 15:24
  • There is nothing to describe "in equations". There are more than one possible orbital, indeed infinitely many of them. As a result an atom can be excited to a higher energy level by absorbing energy in the form of a photon or can deexcite by emitting energy in the form of a photon. How to compute the probability of this happening can be computed using the tools of quantum mechanics, but this would be beyond the scope of your question. – ZeroTheHero Feb 20 '18 at 16:50
  • @ZeroTheHero If H atom has infinitely possible atoms, then how can we ionize any atom? I mean we will give the electron energy and it will just go to a higher orbital but won't leave the atom. – Theoretical Feb 21 '18 at 06:34
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    @Asif While it is true that there are an infinite number of possible states for the electron, the energy spectrum is bounded. As other users have commented, $E_n = -\frac{13.6}{n^2} eV$ where $n \geq 1$. Thus, $-13.6 eV \leq E_n \leq 0$, and if more than $13.6 eV$ energy is gained by the (ground state) electron in hydrogen, it will no longer be bound to the atom and the atom will be ionised. – Styg Feb 21 '18 at 10:25
  • @Samarth Why would it happen? Cant the electron move around the nucleus in a bigger orbital? – Theoretical Feb 21 '18 at 11:10
  • Another way to see this would be the fact that the most probable radius for the electron $\langle r \rangle \propto n^2$, and since $E \rightarrow 0$ as $n \rightarrow \infty$, this means that when given sufficient energy, $\langle r \rangle \rightarrow \infty$. Thus it would be moving around in an infinitely big orbital, so to speak; more accurately, though, the electron will be considered to no longer be bound to the nucleus, hence ionised. – Styg Feb 21 '18 at 13:32
  • @Samarth Thanks for answering all my question. It really helped me a lot. – Theoretical Feb 21 '18 at 13:35
  • There are infinitely many orbitals but they all have finite energy, between -13.6 eV and 0 eV. So you ionize by giving more that 13.6 eV, – ZeroTheHero Feb 21 '18 at 13:36

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The Bohr model does not limit the number of possible orbitals that hydrogen has. At any given time, the single electron is in any one of the possible orbits, sure. But there is no restriction on which orbit it can be in.

Styg
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  • Can you please describe yourself in equations? – Theoretical Feb 20 '18 at 14:26
  • I'm not sure I can express in equations the fact that all the Bohr orbits are valid states (with different energies) for the electron to be in. – Styg Feb 20 '18 at 14:29
  • @AsifIqubal The binding energy of an electron in hydrogen expressed in electronvolt is $E_b = 13.6/n^2$ where $n = 1, 2, 3...$ There is no limit to the principal quantum number $n$. –  Feb 20 '18 at 14:32