# Width of a 1 dimensional box with same ground state energy as hydrogen atom [closed]

I am trying to find the width $L$ of a one-dimensional box for which the ground state energy of an electron in the box equals the absolute value of the ground state of a hydrogen atom.

No measurements (i.e. energy, diameter, mass, etc.) were provided in the question. What are the basics that I need to know about the hydrogen atom in order to solve this question (not including memorizing its ground state energy) ?

## closed as off-topic by ACuriousMind♦, Kyle Kanos, Martin, Qmechanic♦Aug 10 '15 at 11:17

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• First of all, you probably should memorize the ground state energy of the hydrogen atom if you're doing quantum mechanics (both in terms of physical constants and numerically in units of eV). Second, maybe you can tell us what you already know about the hydrogen atom so we can tell you what you're missing. – d_b Aug 9 '15 at 0:03
• For the hydrogen atom, I only know that it carries one electron. Should I then maybe model the atom as an electron in a box to find the width? – mnmakrets Aug 9 '15 at 0:12
• ---- @user37496 – mnmakrets Aug 9 '15 at 0:28
• I think at this level the problem just wants you to equate the energy of the hydrogen ground state to the energy of an electron in its ground state in a finite square well and solve for L. I don't think you are actually supposed to derive the hydrogen atom ground state energy. You are probably safe just looking up what the value is. – d_b Aug 9 '15 at 6:53
• I'd like to recommend you read this meta post on writing good titles. – DanielSank Aug 10 '15 at 3:15

$$E_n = \frac{-13.6 }{n^2}\rm eV$$ (ignore the minus sign for your problem).
$$E_n = \frac{n^2h^2}{8mL^2}$$
Set $n = 1$ to obtain the energies of both ground states. From the identity, solve for $L$ using appropriate units.