Question

Arrange the following species in order of increasing radius. (a) \(\mathrm{Rb}, \mathrm{K}, \mathrm{Cs}, \mathrm{Kr}\) (b) \(\mathrm{Ar}, \mathrm{Cs}, \mathrm{Si}, \mathrm{Al}\)

Short answer

Question: Arrange the given species in each set in order of increasing atomic radius: (a) Rb, K, Cs, Kr and (b) Ar, Cs, Si, Al. Answer: (a) Kr < Rb < K < Cs; (b) Ar < Si < Al < Cs.

Step-by-step solution

(Step 1: Observe trends in the periodic table)

(Take note of the trends in the periodic table: 1. Atomic radius increases as you move down a group due to the addition of electron shells. 2. Atomic radius decreases as you move across a period from left to right due to the increasing nuclear charge, which pulls electrons closer to the nucleus.)

(Step 2: Arrange species a)

(Let's analyze the species in set (a): \(\mathrm{Rb}, \mathrm{K}, \mathrm{Cs}, \mathrm{Kr}\). 1. \(\mathrm{Cs}\) is in the same group as \(\mathrm{Rb}\) and \(\mathrm{K}\), but it is below them in the periodic table. Thus, its atomic radius will be the largest among these three alkali metals. 2. Similarly, \(\mathrm{K}\) is below \(\mathrm{Rb}\) in the periodic table and therefore has a larger atomic radius. 3. \(\mathrm{Kr}\) is a noble gas and is to the right of \(\mathrm{Rb}\) within the same period, so its atomic radius will be smaller than \(\mathrm{Rb}\). Considering these factors, the order of increasing atomic radius in set (a) is: \(\mathrm{Kr} < \mathrm{Rb} < \mathrm{K} < \mathrm{Cs}\).

(Step 3: Arrange species b)

(Now, we will analyze the species in set (b): \(\mathrm{Ar}, \mathrm{Cs}, \mathrm{Si}, \mathrm{Al}\). 1. \(\mathrm{Cs}\) is below \(\mathrm{Si}\) and \(\mathrm{Al}\) and to the left of \(\mathrm{Ar}\) in the periodic table, so its atomic radius is the largest among these species. 2. \(\mathrm{Al}\) is to the left of \(\mathrm{Si}\) within the same period, so it has a larger atomic radius. 3. \(\mathrm{Ar}\) is to the right of \(\mathrm{Si}\) within the same period, so it has a smaller atomic radius. Considering these factors, the order of increasing atomic radius in set (b) is: \(\mathrm{Ar} < \mathrm{Si} < \mathrm{Al} < \mathrm{Cs}\).