Assertion (A): First ionization energy of beryllium is greater than that of boron. Reason (R): Boron has larger size than beryllium. (a) Both \(\mathrm{A}\) and \(\mathrm{R}\) are true and \(\mathrm{R}\) is the correct explanation of \(\mathrm{A}\). (b) Both \(\mathrm{A}\) and \(\mathrm{R}\) are true and \(\mathrm{R}\) is not the correct explanation of \(A\). (c) \(\mathrm{A}\) is true, \(\mathrm{R}\) is false (d) \(\mathrm{A}\) is false, \(\mathrm{R}\) is true

Ionization energy is the energy required to remove the most loosely bound electron from a neutral atom in its gaseous state. The lesser the energy required to remove an electron, the lower will be the ionization energy. There are several factors that affect ionization energy, including nuclear charge, atomic size, and electron shielding.

Across a period in the periodic table, the ionization energy generally increases from left to right. This is due to the increase in the effective nuclear charge experienced by the valence electrons, which pulls them more tightly towards the nucleus and makes it harder to remove these electrons. However, there are some exceptions to this trend, and one of them is the case of beryllium and boron.

Beryllium (Be) has an atomic number of 4 and its electronic configuration is \(1s^2\ 2s^2\). Boron (B) has an atomic number of 5 and its electronic configuration is \(1s^2\ 2s^2\ 2p^1\). To remove an electron from Be, we need to remove one of the 2s electrons. On the other hand, removing an electron from B would involve removing the single 2p electron. Since the 2p electron in B is located farther from the nucleus than the 2s electron in Be, it might be expected that B will have a lower ionization energy than Be. However, electron shielding by the filled 2s orbital in B is less effective than the shielding in Be. As a result, the effective nuclear charge experienced by the 2p electron in B is greater than that experienced by the 2s electron in Be, making it harder to remove the 2p electron in B. Therefore, the Assertion (A) is true.

The Reason (R) given is that "Boron has a larger size than beryllium". This statement is true as atomic size increases while going down a group and decreases while going from left to right in a period. However, this fact alone does not account for the greater ionization energy in beryllium compared to boron, as already discussed in Step 3.

From the analysis above, we can conclude that both Assertion (A) and Reason (R) are true statements. However, the Reason (R) is not the correct explanation for Assertion (A), as the discussion in Step 3 demonstrates. Therefore, the correct answer is (b) Both A and R are true, and R is not the correct explanation of A.