question_answer

The value of ground state energy of hydrogen atom is -13.6 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) As, energy of hydrogen atom is \[-13.6\,eV,\] the negative sign signifies that the electron is bound to the proton (i.e. nucleus of hydrogen atom) or the force acting on the electron is attractive in nature.

(ii) Energy in ground state (n = 1), \[{{E}_{1}}=-13.6\,eV\]

Energy in 1st excited state (n = 2), \[{{E}_{2}}=\frac{-13.6}{{{(2)}^{2}}}\]                                                 \[=-3.4\,eV\] Energy required to take an electron in hydrogen atom from ground state to the first excited state. \[\Delta E={{E}_{2}}-{{E}_{1}}=(-3.4eV)-(-13.6eV)=+10.2eV\]