Question

the photoelectron spectra for h and he are represented above. which of the following statements best accounts for the fact that the peak on the he spectrum is farther to the left and higher than the peak on the h spectrum? a he has an additional valence electron in a higher energy level than the valence electron in h. b he has a greater nuclear charge than h and an additional electron in the same energy level. c he has a completely filled valence shell in which the electrons are a greater distance from the nucleus than the distance between the h nucleus and its electron. d it takes longer for the electrons in he to be removed due to the higher nuclear mass of he.

Explanation:

• Option A: Helium (\(He\)) has 2 electrons in the \(1s\) orbital (valence shell), hydrogen (\(H\)) has 1 electron in the \(1s\) orbital. They are in the same energy level (\(n = 1\)), so this option is incorrect.
• Option B: Helium has an atomic number \(Z=2\) (nuclear charge \(+ 2\)), hydrogen has \(Z = 1\) (nuclear charge \(+1\)). According to Coulomb's law \(F=\frac{kq_1q_2}{r^{2}}\) (where \(q_1\) is nuclear charge, \(q_2\) is electron charge), the greater nuclear charge of \(He\) attracts its electrons more strongly. The binding energy of electrons (related to the energy in the photoelectron spectrum) is higher for \(He\) due to stronger electrostatic attraction.
• Option C: Both \(H\) and \(He\) electrons are in the \(1s\) orbital (closest to the nucleus for their atoms). The distance of \(1s\) electrons from the nucleus is not the reason for the difference in the photoelectron spectra peak positions as described.
• Option D: Nuclear mass does not directly affect the binding energy of electrons in the way described for photoelectron spectra. The electrostatic interaction (nuclear charge - electron charge) is the key factor for electron binding energy in photoelectron spectroscopy.

Answer:

B. He has a greater nuclear charge than H and an additional electron in the same energy level.