Correct Answer - Option 2 : S
Concept:
Bohr's atomic model.
- The electrons revolve around the nucleus in circular orbits with discrete energy, i.e, the energy is quantized.
- The radius of the orbits is also fixed.
- When electrons are supplied with energy, they jump to higher orbitals.
- The angular momentum of the electrons is quantized and given by
\(mvr = \frac{{nh}}{{2\pi }}\).
- The frequency of light ν required to transition of an electron that differs in energy by
\(\Delta E\;isequal\;to = \frac{{\Delta E}}{h} = \frac{{hν '' - hν '}}{h} = ν \;\;\) where hν'' and hν' is the energy of higher and lower orbitals respectively.
- The Energy of an electron in a stationary orbit is given by:
\(-e^2\over {8 πε_0r}\)
\(E_n = - R_H\frac{{Z^2}}{{n^2}}\)
When expressed in electron volts, the energy of an electron in an orbit is given by:
\(E_n = - 13.6\frac{{Z^2}}{{n^2}}eV\)
Explanation:
- The s- orbital has a symmetrical shape and the electron cloud is more concentrated in it.
- As the s-orbital thus resides closest to the nucleus, radius ' r ' is the smallest for 's ' orbital.
- Being closer to the nucleus, it experiences a greater amount of nuclear charge from the protons of the nucleus.
- As we move on from s to d, the orbitals become more diffused in nature and electron density becomes less.
- The distance from the nucleus also increases accordingly.
- The energy of an electron is given by:
\(-e^2\over {8 πε_0r}\)
The magnitude of the negative value of energy is inversely proportional to the radius of the orbital.
As radius 'r' is smallest for ' s ' orbital, the negative energy is the highest.
Correspondingly, the electrons in s orbital will have the maximum negative energy value.
Hence, for a given shell in an atom, s orbital electrons will have the maximum negative energy value.
