If the ionisation energy for the hydrogen atom is 13.6 eV, then the energy required to excite it from the ground state to the next higher state is nearly

Step-by-step solution

The energy of an electron in the n -th orbit of a hydrogen atom is given by E_n = - 13.6 n^2 eV . For the ground state ( n=1 ), the energy is E₁ = -13.6 eV . For the next higher state ( n=2 ), the energy is E₂ = - 13.6 2^2 = -3.4 eV . The energy required for excitation from the ground state to the first excited state is E = E₂ - E₁ . Substituting the values, E = -3.4 - (-13.6) = 10.2 eV .