To calculate the energy difference between the ground state and first excited state of an H2 molecule, we can use the time-dependent Schrödinger equation. However, solving the Schrödinger equation for a multi-electron system like H2 is quite complex and requires advanced computational methods. Instead, we can use some experimental data and approximations to estimate the energy difference and the resulting wavelength of light absorbed or emitted during the transition.The energy levels of the H2 molecule can be approximated using the molecular orbital theory. In this theory, the ground state of the H2 molecule is represented by the bonding molecular orbital 1g formed by the overlap of the 1s orbitals of the two hydrogen atoms. The first excited state is represented by the antibonding molecular orbital 1u* formed by the out-of-phase combination of the 1s orbitals.The energy difference between these two states can be estimated using the ionization energy IE and electron affinity EA of the hydrogen atom:E = IE - EAFor the hydrogen atom, the ionization energy is approximately 13.6 eV, and the electron affinity is approximately 0.75 eV. Therefore, the energy difference between the ground state and the first excited state is:E 13.6 eV - 0.75 eV 12.85 eVNow, we can use the energy difference to calculate the wavelength of light absorbed or emitted during the transition using the Planck's equation:E = h * c / Where E is the energy difference, h is the Planck's constant 6.626 x 10^-34 Js , c is the speed of light 3 x 10^8 m/s , and is the wavelength.Rearranging the equation to solve for : = h * c / EPlugging in the values: 6.626 x 10^-34 Js * 3 x 10^8 m/s / 12.85 eV * 1.602 x 10^-19 J/eV 9.65 x 10^-8 m 96.5 nmSo, the wavelength of light absorbed or emitted during the transition between the ground state and the first excited state of an H2 molecule is approximately 96.5 nm. This falls in the ultraviolet UV region of the electromagnetic spectrum.