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It increases across down a group because the elements have valence electrons in the same orbital, but the ones further down have more electrons in the same orbital, thus increasing its attraction to the nucleus. For this reason, it’s really hard to remove an electron. Increasing across a period, the valence shells are becoming more and more full. It then wants to gain electrons more than lose them, which is why ionization energy increases for that. Hope that helps with the first bit.
Ionization energy is the energy needed to remove an electron from an atom and electron affinity is the energy released when an electron is added to a gas-phase atom. Ionization energy increases down a period because an atom that only needs to lose one electron to form an octet, would require less energy than an atom that needs to lose three electrons to form an octet. It decreases down a group because of electron shielding from other shells of electrons. Electron affinity trends are the same and a good rule of thumb is that there is a generally high electron affinity for elements in the top right of the periodic table.
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