Energy required by an electron to move from ground state to 3rd excited state of He ion

To determine the energy required for an electron to move from the ground state to the 3rd excited state of a helium ion, we need to consider the energy levels of the ion and calculate the difference between these levels.

Energy Levels of He+ ion
The energy levels of a helium ion (He+) are determined by the electron configuration. Since a helium ion has lost one electron compared to a neutral helium atom, the electron configuration of He+ is 1s2.

The energy levels of He+ ion can be represented as follows:
1s, 2s, 2p, 3s, 3p, 3d, ...

Ground State and 3rd Excited State
The ground state of He+ ion corresponds to the 1s energy level, while the 3rd excited state corresponds to the 3p energy level.

Energy Difference Calculation
To calculate the energy difference between the ground state and the 3rd excited state, we need to subtract the energy of the ground state from the energy of the 3rd excited state.

The energy of an electron in a hydrogen-like atom/ion can be calculated using the formula:
E = -13.6/n^2 electron volts (eV)

For the ground state (n=1), the energy is:
E1 = -13.6/1^2 = -13.6 eV

For the 3rd excited state (n=3), the energy is:
E3 = -13.6/3^2 = -13.6/9 = -1.51 eV

To calculate the energy difference, we subtract the energy of the ground state from the energy of the 3rd excited state:
ΔE = E3 - E1 = (-1.51) - (-13.6) = 12.09 eV

Conclusion
The energy required by an electron to move from the ground state to the 3rd excited state of a helium ion is 12.09 eV. Therefore, none of the given options (1) 51 eV and 2) 40.8 eV) is correct.