Question

The binding energy of an electron in the ground state in a hydrogen atom is about:

A. 13.6 eV

B. 3.4 eV

C. 10.2 eV

D. 1.0 eV

E. 27.2 eV

Answer 1

ANS: (A)= 13.6eV

According to the theory quantum mechanics, an electron bound to an atom can not have any value of energy, rather it can only occupy certain states which correspond to certain energy levels. The formula defining the energy levels of a Hydrogen atom are given by the equation: E = -E0/n2, where E0 = 13.6 eV (1 eV = 1.602×10-19 Joules) and n = 1,2,3… and so on. The energy is expressed as a negative number because it takes that much energy to unbind (ionize) the electron from the nucleus. It is common convention to say an unbound electron has zero (binding) energy. Because an electron bound to an atom can only have certain energies the electron can only absorb photons of certain energies exactly matched to the energy difference, or “quantum leap”, between two energy states.

When an electron absorbs a photon it gains the energy of the photon. Because an electron bound to an atom can only have certain energies the electron can only absorb photons of certain energies. For example an electron in the ground state has an energy of -13.6 eV. The second energy level is -3.4 eV. Thus it would take E2 ? E1 = -3.4 eV ? -13.6 eV = 10.2 eV to excite the electron from the ground state to the first excited state

If a photon has more energy than the binding energy of the electron then the photon will free the electron from the atom – ionizing it. The ground state is the most bound state and therefore takes the most energy to ionize.