An H$2$ molecule can be approximated by a simple harmonic oscillator having a spring constant

k $=1\mathrm{.}10103$ N$/$m$.$

$($a$)$

How many different energy transitions are possible when the H$2$ molecule decays from the third excited state down to the ground state?

$3$

$($b$)$

Find the photon energies $($in eV$)$ produced in these transitions and their wavelengths $($in nm$).$ Enter $0$ in any unused boxes.

relative energytransition energywavelengthslowest$0\mathrm{.}753$ eV$1642\mathrm{.}3$ nmmiddle$1\mathrm{.}5$ eV$821\mathrm{.}1$ nmhighest$2\mathrm{.}26$ eV$547\mathrm{.}4$ nm