Problem 11 - Chemistry A Guided Inquiry

Question

Which of the following systems will have the larger ionization energy? Explain your reasoning. a) an electron at a distance \(d_{1}\) from a nucleus with charge \(+2\) b) an electron at a distance \(d_{1}\) from a nucleus with charge \(+1\)

Step-by-Step Solution

Answer

The system comprising of an electron at a distance \(d_{1}\) from a nucleus with charge \(+2\) will have a larger ionization energy.

Step 1: Identifying Given Variables

In both cases, the distance (d) of the electron from the nucleus is the same. The nuclear charges differ, with the first being +2 and the second being +1.

Step 2: Understanding The Relationship of Variables

The ionization energy depends on the force of attraction between the electron and the nucleus. This force is given by Coulomb's law which states that force is directly proportional to the product of charges and inversely proportional to square of distance between them. Here, distance being same in both cases, more the nuclear charge, more will be the force of attraction hence greater the ionization energy.

Step 3: Making The Comparison

Therefore, since the nucleus with charge +2 has a stronger attractive force on the electron than the nucleus with charge +1, it will have a higher ionization energy. This means that removing an electron from the +2 nucleus will require more energy than from the +1 nucleus.