Answer to Question #95339 in Physics for Bruno

Question

Explain with examples, why;

i) atomic radius increases as you go down the group and decreases as you go across a period?
ii) the main trend for first ionization energy to increase across periods?
iii) the value of first electron affinity of oxygen (-142 kJ/mol) smaller than that of fluorine
(-328 kJ/mol)?

Answer 1

The answer for the first two questions is because the elements were arranged exactly this way by scientists. Elements from one group have more and more electron shells as you go down the group, so, since atoms are electrically neutral, there must be the same number of positive charges (protons) to compensate the total negative charge. For instance, compare $^{24}_{12}\text{Mg}$ with $^{40}_{20}\text{Ca}.$ We see that calcium has more electrons, more protons, therefore, larger nucleus, that is why it is lower than magnesium. The atomic radius decreases as you go across a period because the charge of nucleus increases from left to right and this causes the electron shells to be attracted closer to the nucleus (compare calcium with $^{80}_{35}\text{Br}$).

The ionization energy increases across periods because the electrons are closer to the nucleus (because there are more positive charges attracting them), and according to Coulomb's law, the smaller the distance - the stronger the attraction. That is why you need to spend more energy to tear the electron out of its shell. It is 589.4 kJ/mol for Ca and 800.2 kJ/mol for Br.

First electron affinity of oxygen (-142 kJ/mol) is smaller than that of fluorine (-328 kJ/mol) because oxygen has 1 proton less than fluorine (8 vs. 9), while the screening is the same.