Chemistry

Problem

Element R is in the same period as element S. Both are main-group elements in their ground-state gaseous atoms. A chemist has determined the following average values for their outermost electrons:

Quantity	R	S
Effective nuclear charge, $Z_{\text{eff}}$	4.1	3.2
Average radius of the outermost electron, $r$ (pm)	95	115

Assume that the first ionization energy

I_1

is approximately proportional to

\dfrac{Z_{\text{eff}}}{r^2}

. (a) Using the proportionality, calculate the ratio

\dfrac{I_{1}(\text{R})}{I_{1}(\text{S})}

to two significant figures. (b) Identify which element, R or S, has the higher first ionization energy and provide a brief explanation that refers to both

Z_{\text{eff}}

and

r

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