Answer
$L = 0.426~nm$
Work Step by Step
We can find the energy of the photon:
$E = \frac{h~c}{\lambda}$
$E = \frac{(6.626\times 10^{-34}~J~s)(3.0\times 10^8~m/s)}{600\times 10^{-9}~m}$
$E = 3.313\times 10^{-19}~J$
We can find the length of the box:
$E_n = \frac{n^2~h^2}{8~m~L^2}$
$E_1 = \frac{1^2~h^2}{8~m~L^2}$
$L^2 = \frac{h^2}{8~m~E_1}$
$L = \frac{h}{\sqrt{8~m~E_1}}$
$L = \frac{6.626\times 10^{-34}~J~s}{\sqrt{(8)~(9.109\times 10^{-31}~kg)~(3.313\times 10^{-19}~J)}}$
$L = 4.26\times 10^{-10}~m$
$L = 0.426~nm$
