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6. *) Multi-electron systems: 6.1 The X-ray photoelectron spectrum of an unknown element X shows in his

Emission spectrum based on four clearly different kinetic energies:

5.9 x 10-17 J; 2.53 x 10-18 J; 2.59 x 10-20 J, and 2.67 x 10-20 J

(Assume that the X-rays have enough energy to destroy each

To knock out an electron from an atom.)

i) Name all possible atoms in their electronic ground state that a

could deliver such a spectrum.

ii) Calculate the binding energy of an electron in the 2p orbital of element X, if

the X-rays used in this experiment have an energy of 2.68 · 10-16 J

own. 6.2 To ionize phosphorus, the following ionization energies are required: 1. Ionization energy: 1011 kJ / mol

2. Ionization energy: 1903 kJ / mol

3. Ionization energy: 2912 kJ / mol

i) Use this information to calculate the effective nuclear charge (Zeff), which is applied to the 3p Electron works! ii) What would you expect? Is the minimum energy needed to get a 3s electron

to knock out of the phosphorus atom in a photoelectron experiment, bigger, less than or equal to the 4th ionization energy of the phosphorus atom? Briefly explain your reasons Answer!

Answer :

The kinetic energies in the X-ray photoelectron spectrum indicate the binding energies of electrons in the unknown element X. Without this information, we cannot calculate the binding energy of the 2p electron for element X.

By comparing these energies to the known binding energies of electrons in different elements, we can determine the possible atoms in their electronic ground state that could produce such a spectrum. To do this, we need to match the kinetic energies to the binding energies of electrons in various elements. Unfortunately, the specific binding energies corresponding to the given kinetic energies are not provided in the question. Without this information, we cannot accurately determine the possible atoms that would produce this spectrum. The binding energy of an electron in the 2p orbital of element X can be calculated by subtracting the energy of the X-ray used in the experiment (2.68 × 10^-16 J) from the kinetic energy of the corresponding photoelectron (given in the spectrum). Since the energy of the X-ray corresponds to the energy required to remove an electron from the 2p orbital, the difference will give us the binding energy of the electron in the 2p orbital of element X.Unfortunately, the specific kinetic energy corresponding to the 2p electron is not provided in the question. Without this information, we cannot calculate the binding energy of the 2p electron for element X.

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