The outermost valence electron in atom A experiences an...

The outermost valence electron in atom A experiences an effective nuclear charge of $2+$ and is on average $225 \mathrm{pm}$ from the nucleus. The outermost valence electron in atom B experiences an effective nuclear charge of $1+$ and is on average $175 \mathrm{pm}$ from the nucleus. Which atom (A or B) has the highest first ionization energy? Explain.

Key Concepts

Ionization Energy

Ionization energy is the energy required to remove an electron from an atom. It depends largely on the effective nuclear charge and the distance of the electron from the nucleus; a higher effective nuclear charge and a shorter distance generally lead to a higher ionization energy.

Atomic Radius

The atomic radius refers to the average distance of the outermost electrons from the nucleus. An increased distance means the electron is less tightly held, which typically lowers the ionization energy, whereas a smaller radius generally results in a stronger attraction between the nucleus and the electron.

Effective Nuclear Charge

This is the net positive charge experienced by an electron in an atom after accounting for shielding by other electrons. It is a crucial factor in determining how strongly an electron is attracted to the nucleus, and thus directly influences properties such as ionization energy.

Transcript

0:00 Question.

00:02 We have two atoms, and one has an effective nuclear charge of plus two, and the distance of 225 picometers between the balanced electron and the nucleus.

00:18 For atom b, we have an effective nuclear charge of plus one, and the average distance between the outermost valence electron and the nucleus 175.

00:26 We want to know which one has the highest first ionization energy.

00:29 So what we are going to do is we are going to use coulom's law in order to determine this.

00:40 So coulom's law can be written like this.

00:51 So if we multiply both sides by r, we get force times distance.

00:56 So force times distance is equal to work done, which is equal to potential energy.

01:04 So we can write the following.

01:07 So from this, we can use this to calculate the potential energy between the two charges in these atoms.

01:22 The charge of an electron and proton is going to be 1 .6 times 10 to the negative 19 coolums.

01:30 So we only need to care about the absolute value in this case, because we're only looking at the value of the potential energy.

01:36 In both cases, it will actually be negative, and i've explained that here.

01:41 But for simplification purposes, we actually would just need to look at the absolute value.

01:49 So we have an effect nuclear charge of two.

01:52 So let's multiply the charge of one proton by two, and we get the charge in coolums that we experience from, that the electron experiences in atom a.

02:07 So let's do this calculation for atom a.

02:09 So we plug in the values into the formula...

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