Question

The orbital degenrancy of the level of one electron atomic system with Z= 5 and energy - 13.6eV is?
a) 1
b) 5
c)25
d) 36​

Answer 1

Answer:

The correct answer is option (c) $25$.

Explanation:

For a one-electron atomic system with atomic number Z, the energy of the electron in the nth energy level is given by the formula:

$E = - (13.6 eV) Z^2 / n^2$

Here, $Z = 5 and E = -13.6 eV$.

Therefore, we can solve for n as follows:

$n^2 = - (13.6 eV) (5^2) / (-13.6 eV)\\n^2 = 25\\n = 5$

So the electron is in the fifth energy level. The orbital degeneracy for a given energy level is equal to the number of orbitals at that energy level. For the nth energy level, the number of orbitals is given by $n^2$. Therefore, for the fifth energy level, the number of orbitals is:

$n^2 = 5^2 = 25$

So the orbital degeneracy for the fifth energy level of a one-electron atomic system with $Z = 5$ is $25$.

Therefore, the correct answer is option (c) $25$.

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