Which one of the following about an electron occupying the 1s-orbital in a hydrogen atom is incorrect? (The Bohr radius is represented by a₀)

Moderate

A

The electrons can be found at a distance 2a₀ from the nucleus.
B

The magnitude of the potential energy is double that of its kinetic energy on an average.
C

The probability density of finding the electron is maximum at the nucleus.
D

The total energy of the electron is maximum when it is at a distance a₀ from the nucleus.

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 (a₀) 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. a₀). But the electron can be found at a distance at 2a₀ 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 (R²) 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 a₀ from the nucleus.
Because at a₀ electron is at stable position and we known that if a electron acquired stability the its energy is minimum.

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