Questions

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})

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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.

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detailed solution

Correct option is D

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 eVK.E value = 13.6 eVSo, 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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