# How does energy levels of an electron differ from atoms?

I would like to know how does energy levels of an electron differs from atom. I've read that electrons with almost similar energy orbit in the same orbital and have a discrete set of energy levels. How are energy levels represented in atoms?

• I presume that you are asking about some difference between the energy levels of an atom and those of an electron whereas they are actually all the same and it is better to call them as energy levels of an atom, if that is your question BTW. – SchrodingersCat Dec 28 '15 at 11:04
• What energy level of atoms? – N.S.JOHN Dec 28 '15 at 11:56

If by an electron you mean a free electron then that can take on any energy value: the spectrum of allowed energy values is continuous.

In atoms, electrons are bound by the electrostatic attraction exerted by the nucleus. The total energy function (the Hamiltonian) of an electron in a hydrogen atom is described by the Schrödinger equation.

Solving it yields the eigenfunctions (wave functions) $\Psi_{n,l,m}$ and the assorted eigenvalues $E_{n,l,m}$.

The allowed energy levels can be found here and (disregarding the fine structure) is given by the formula:

$$E_n=-\frac{13.6\:\mathrm{eV}}{n^2}$$

Where $n$ is the Principal Quantum Number $(n=1,2,3,4,...)$. The energy spectrum of an electron in a hydrogen atom is thus discrete and not continuous.

For multi-electronic atoms this principle holds but the Schrödinger equation can no longer be solved analytically (numerical methods are needed).

Atoms are quantum systems comprised of a nucleus and electrons: the energy spectrum obtained by solving the Schrödinger equation is the energy spectrum of the system, i.e. the atom itself.

• :That's great for electrons.Like this is there any energy level representation for atom? – justin Dec 29 '15 at 6:27
• The representations are those of the atom because nucleus + electron form one system. – Gert Dec 29 '15 at 14:11
• :Do you mean to say that the energy representation for electron and atom is same? – justin Dec 30 '15 at 6:27
• @justin: basically yes. $E$ is the total energy of the atom (electron + nucleus). This true of all systems: the potential energy of an object is the PE of object + object that causes the central field. – Gert Dec 30 '15 at 15:27
• :I think it's better to update your answer with mentioning that energy representation for electron and atom is the same. – justin Dec 31 '15 at 6:19