Calculating Energy Levels in an Infinite Potential Box: Converting to eV?

[leonne]

Homework Statement

well the problem is electron moving in an infinite poentail box of dimensions... calc all posible energy level in (eV)

Homework Equations

E=h²/8M(n_x²/a²+...

The Attempt at a Solution

ok so no idea how they get h²/8M to = 37.6 h is planks constant the units are in m⁴kg s^-2 but eV is in m²kg s^-2 don't see how they get 37.6 for mass i used 9.11e-31

 

[Pengwuino]

Find out the energy levels in Joules and simply use the conversion between Joules and eV. Should be easily google'd/wikipedia'ed or should be in your textbook.

 

[vela]

There are some useful combinations of the fundamental constants. If you know them, you can make calculations a lot faster.
\begin{align*}
h c &= 1240~\text{eV nm} \\
\hbar c &= 197~\text{eV nm} = 197~\text{MeV fm} \\
m_e c^2 &= 511000~\text{eV} = 511~\text{keV} = 0.511~\text{MeV}
\end{align*}
For your problem, you just need to introduce factors of c, the speed of light, to form the right combinations:
$$\frac{h^2}{8m} = \frac{(hc)^2}{8mc^2} = 0.376~\text{eV nm}^2$$Note that this combination has two powers of length. They are needed to cancel the units from a² in the denominator of the formula for the energy.