Question

why do atoms of different elements have different ionization energies?
ionization energy depends upon the strength of the attractive force between
the positively charged nucleus and a negatively charged electron. the stronger
the attractive force, the more difficult it is to remove the electron from the
atom—and the greater the ionization energy.
according to coulombs law, the strength of this attractive force depends on
two competing factors: the amount of positive charge from the nucleus and
the distance between the electron and the nucleus. the force of attraction
between an electron and an atoms nucleus increases as the positive charge
increases. the attractive force decreases as the distance between the electron
and the nucleus increases.
each of these models shows a nucleus (yellow) with its charge and an electron
(blue) some distance away. in which of these models would the attractive
force between the nucleus and the electron be the weakest?

Explanation:

Step1: Analyze the effect of nuclear charge

According to Coulomb's law, the force of attraction \(F\propto\frac{q_1q_2}{r^{2}}\) (where \(q_1\) is the charge of the nucleus, \(q_2\) is the charge of the electron (\(- 1e\)), and \(r\) is the distance between them). For a given distance \(r\), a smaller nuclear charge (\(q_1\)) will lead to a smaller force.

Step2: Analyze the effect of distance

For a given nuclear charge \(q_1\), a larger distance \(r\) will lead to a smaller force since \(F\propto\frac{1}{r^{2}}\).

Comparing the four models:

• Model 1: \(q_1 = 14e\), \(r\) (distance) - shorter
• Model 2: \(q_1=10e\), \(r\) (distance) - shorter
• Model 3: \(q_1 = 14e\), \(r\) (distance) - longer
• Model 4: \(q_1=10e\), \(r\) (distance) - longer

Since \(F\propto\frac{q_1}{r^{2}}\), for model 4, with the smallest \(q_1\) (\(10e\)) and the largest \(r\) (compared to model 2), the force of attraction will be the weakest.

Answer:

The model with a \(10 +\) nucleus (charge \(q_1 = 10e\)) and the longest distance between the nucleus and the electron (model 4) has the weakest attractive force.