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# Engineering

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

  • Option 1)

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

  • Option 2)

    The electron can be found at a distance 2a_{o} from the nucleus.

  • Option 3)

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

  • Option 4)

    The total energy of the electron is maximum when it is at a distance a_{o} from the nucleus.

Answers (1)
S solutionqc

 

Total energy of elctron in nth orbit -

E_{n}= -13.6\: \frac{z^{2}}{n^{2}}eV

Where z is atomic number

-

 

 

 

a. \Psi ^{2}\propto r, so probability density of finding the electron is maximum at the nucleus .

 

b. True, the electron can be found at any distance from the nucleus.

c.  \left | P.E. \right |=2\left | K.E. \right |  on average.

d.  E=-13.6\frac{z^{2}}{n^{2}}ev,\:\:E_{1}=\frac{-13.6}{r}\:\:\:ev=\frac{-13.6}{a_{o}}

      E_{2}=\frac{-13.6}{2a_{o}}

       \left ( E_{2}>E_{1} \right )

E_{1} is minimum not maximum

(d) is incorrect.

 


Option 1)

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

Option 2)

The electron can be found at a distance 2a_{o} from the nucleus.

Option 3)

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

Option 4)

The total energy of the electron is maximum when it is at a distance a_{o} from the nucleus.

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