Atomic Orbitals

Question

Which one of the following about an electron occupying the 1s-orbital in a hydrogen atom is incorrect? (The Bohr radius is represented by a_{0})

Moderate

Solution

Statement (4) is incorrect.

(a) The radial distribution curve obtianed by plotting radial probability functions vsr for 1s-orbital is

The graph initially increases and then decreases. It reaches a maximum at a distance (a_{0}) very close to the nucleus and then decreases. The maximum in the curve corresponds to the distance at which the probability of finding the electron in maximum (i.e. a_{0}). But the electron can be found at a distance at 2a_{0} also from the nucleus.

(b) The P.E. value = -27.2 eV

K.E value = 13.6 eV

So, the magnitude of PE is double that of its kinetic energy on an average.

(c) For 1s-orbital radial probability density (R^{2}) against r is given as

For 1s-orbital, probability density decreases sharply as we move away from nucleus. Thus, the probability density of finding the electron is maximum at the nucleus.

(d) Correct statement (d) is : The total energy of the electron is minimum when it is at a distance a_{0} from the nucleus.

Because at a_{0} electron is at stable position and we known that if a electron acquired stability the its energy is minimum.

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