question_answer

The energy of the electron in the ground state of hydrogen atom is -\[\mathbf{13}.\mathbf{6}\text{ }\mathbf{eV}.\] (i) What does the negative sign signify? (ii) How much energy is required to take an electron in this atom from the ground state to the first excited state?          

Answer:

                (i) The negative sign indicates that the electron is bound to the nucleus by electrostatic forces of attraction. (ii) Energy in ground state, \[{{E}_{1}}=-13.6eV\] Energy in first excited state, \[{{E}_{2}}=-\frac{13.6}{{{2}^{2}}}=-3.4eV\] Required energy, \[\Delta E={{E}_{2}}-{{E}_{1}}\] \[=-3.4+13.6=\mathbf{10}\mathbf{.2eV}.\]