Question

the table shows the first, second, and third ionization energies of four elements of period 6. one of the elements is a noble gas. from the information in the table, which option, reading in order from left to right, correctly completes the sentences? an element may be chosen more than once or not at all. the noble gas is most likely element —. of the four, element — has the largest atomic radius. the element which would form cations with a 2 + charge is —. 1 3 2 4 2 1 4 2 3 4 2 3 3 3 4

Explanation:

Step1: Determine the Noble Gas

Noble gases have very high ionization energies as they have stable electron configurations. Looking at the first ionization energies, Element 1 has the highest first - ionization energy (\(812\) kJ/mol). So, the Noble Gas is Element 1.

Step2: Determine the element with the largest atomic radius

Atomic radius generally decreases across a period. Lower first ionization energy usually corresponds to a larger atomic radius (as the outermost electrons are more loosely held). Element 2 has the lowest first ionization energy (\(376\) kJ/mol), so Element 2 has the largest atomic radius.

Step3: Determine the element that forms \(2 +\) cations

For an element to form a \(2+\) cation, the second - ionization energy should be relatively low compared to the third - ionization energy.

• For Element 3: \(\frac{IE_{2}}{IE_{1}}=\frac{965}{503}\approx1.92\), \(\frac{IE_{3}}{IE_{2}}=\frac{3458}{965}\approx3.58\)
• For Element 2: \(\frac{IE_{2}}{IE_{1}}=\frac{2234}{376}\approx5.94\)
• For Element 4: \(\frac{IE_{2}}{IE_{1}}=\frac{2060}{1037}\approx1.99\), \(\frac{IE_{3}}{IE_{2}}=\frac{2840}{2060}\approx1.38\) (not a big jump)
• For Element 1: It is a noble gas and does not easily form cations.

Element 3 has a relatively small increase from \(IE_{1}\) to \(IE_{2}\) and a large increase from \(IE_{2}\) to \(IE_{3}\). The ratio of \(IE_{2}/IE_{1}\) is not too large (indicating it can lose the second electron relatively easily) and \(IE_{3}/IE_{2}\) is large (indicating it is difficult to lose the third electron). So the cation with \(2 +\) charge is from Element 3.

The sequence is Noble Gas (Element 1), largest atomic radius (Element 2), \(2+\) cation (Element 3), so the order is \(1,2,3\)

Answer:

\(1,2,3\)