# Why is the energy of an electron always negative?

I just wrote my chemistry exam a few hours ago. However, I am still confused about the following question:

Why is the energy of an electron in an orbital always negative?

I wrote that from the following equation

$$E_n = -R_h\left(1-\frac{1}{n^2}\right),$$

we can see that the energy will always be negative.

• It is right, but does not actually explain anything. Sep 8 '16 at 10:31
• Energy of electron in n th orbit. Sep 8 '16 at 10:44
• Since Rydbergs constant is negative Sep 8 '16 at 10:45
• Energy too negatuve Sep 8 '16 at 10:45
• Technically it is a physics.se question. Commonly energy of electron in a molecule/ion is measured relatively to free electron in vacuum, which is assumed to be zero. Since electron in orbit needs to have energy lower than that in vacuum, or it shall leave the particle, it is lower than zero. Typically it happens thanks to interaction with positive charge of atomic nucleus. Thus, the answer for your question is: because otherwise it shall leave the particle. Sep 8 '16 at 12:29

To be precise, Rydberg's constant is $$R_{\infty}=\frac{m_ee^4}{8\epsilon_0^2h^3c}$$ where all those constants have their usual meanings. Importantly, all of those constants are manifestly positive.
Whether the energy is positive or negative is entirely arbitrary. The energy of an electron can also be formulated as, $$E_n=R_h(1-\frac{1}{n^2}).$$
The only difference between the equation you wrote down and the one I just wrote down is that the above equation sets the zero of energy at the ground state of the hydrogen atom. You'll see that when $n=1$ the energy is zero and as $n\to\infty$ the energy approaches the Rydberg constant which is the ionization energy of the hydrogen atom.