To calculate the energy difference between the ground state and the first excited state of a hydrogen atom, we can use the Rydberg formula for the energy levels of a hydrogen atom. The formula is:E_n = -13.6 eV * Z^2 / n^2 where E_n is the energy of the electron in the nth energy level, Z is the atomic number Z = 1 for hydrogen , and n is the principal quantum number.For the ground state n = 1 , the energy is:E_1 = -13.6 eV * 1^2 / 1^2 = -13.6 eVFor the first excited state n = 2 , the energy is:E_2 = -13.6 eV * 1^2 / 2^2 = -3.4 eVNow, we can calculate the energy difference between the ground state and the first excited state:E = E_2 - E_1 = -3.4 eV - -13.6 eV = 10.2 eVSo, the energy difference between the ground state and the first excited state of a hydrogen atom is 10.2 eV.