To calculate the energy difference between the ground state n1 = 1 and the first excited state n2 = 2 of the hydrogen atom, we can use the Rydberg formula for energy levels:E = -13.6 eV * 1/n^2 where E is the energy of the electron in the hydrogen atom, n is the principal quantum number, and 13.6 eV is the ionization energy of hydrogen.First, let's calculate the energy of the ground state n1 = 1 :E1 = -13.6 eV * 1/1^2 = -13.6 eVNow, let's calculate the energy of the first excited state n2 = 2 :E2 = -13.6 eV * 1/2^2 = -13.6 eV * 1/4 = -3.4 eVFinally, let's find the energy difference between the ground state and the first excited state:E = E2 - E1 = -3.4 eV - -13.6 eV = 10.2 eVSo, the energy difference between the ground state and the first excited state of the hydrogen atom is 10.2 electron volts eV .