Chapter 4.4, Problem 4.4.5SR

Which pair of opposite charges has the greatest attractive force?

(a) +1 and −1 separated by 1.0 pm

(b) +1 and −3 separated by 2.0 pm

(c) +2 and −2 separated by 1.5 pm

(d) +3 and −3 separated by 2.5 pm

(e) +3 and −3 separated by 3.0 pm

Interpretation Introduction

Interpretation: From the given choices the correct choice that contains charges with larger force of attraction should be determined.

Concept Introduction:

Coulombs law: It states that the force of attraction between two point charges is directly proportional to the product of the point charges and inversely proportional the square of the distances between the charges.

$\begin{array}{l}F\propto \frac{Q_1\times Q_2}{d^{\text{2}}}\\ Q_1,Q_2\to \text{Given point charges}\\ d\to \text{distance between the charges}\end{array}$

Valence electron: The electron is considered as valence electron if it present in outermost shell of atom which gets involved in the formation of chemical bond.

Effective nuclear charge: It is the overall positive charge experienced by the outermost electrons present in the atom from the nucleus of the atom.

Screening Effect: The core electrons present near the nucleus shields the outermost electrons (valence electrons) from the charge of the nucleus.

Answer to Problem 4.4.5SR

Answer

The two charges that have larger force of attraction is as follows,. $\text{(c)}\text{+2}\text{and}\text{-2}\text{separated}\text{by}\text{1}\text{.5}\text{pm}\text{.}$

Explanation of Solution

Explanation

Reason for correct option

Determine the force of attraction for the two given charges +2 and -2.

$\begin{array}{l}\text{Given Data,}\\ {\text{Q}}_{\text{1}}\text{ = +2}\\ {\text{Q}}_2\text{ = -2}\\ \text{Distance }\left(d\right)\text{ = 1}\text{.5pm}\end{array}$

$\begin{array}{l}\text{The force of attraction for the two given charges,}\\ F\propto \frac{2\times \left(-2\right)}{{\left(\text{1}\text{.5pm}\right)}^2}\\ =-1.78\end{array}$

The force of attraction for given charges separated by distance of 1.5 pm is determined by substituting the charges and the distance values to the given formula results to give the value for force of attraction.

Therefore, the charge with larger force of attraction is $\text{(c)}\text{+2}\text{and}\text{-2}\text{separated}\text{by}\text{1}\text{.5}\text{pm}\text{.}$.

Hence, the correct option is option c.

Reasons for incorrect options:

Consider all options other than the correct one and determine the force of attraction.

$\begin{array}{l}\text{Given Data,}\\ {\text{Q}}_{\text{1}}\text{ = +1}\\ {\text{Q}}_2\text{ = -1}\\ \text{Distance }\left(d\right)\text{ = 1}\text{.0pm}\end{array}$

$\begin{array}{l}\text{The force of attraction for the two given charges,}\\ F_a\propto \frac{1\times \left(-1\right)}{{\left(\text{1}\text{.0pm}\right)}^2}\\ =-1\end{array}$

$\begin{array}{l}\text{Given Data,}\\ {\text{Q}}_{\text{1}}\text{ = +1}\\ {\text{Q}}_2\text{ = -3}\\ \text{Distance }\left(d\right)\text{ = 2pm}\end{array}$

$\begin{array}{l}\text{The force of attraction for the two given charges,}\\ F_b\propto \frac{1\times \left(-3\right)}{{\left(\text{2pm}\right)}^2}\\ =-0.75\end{array}$

$\begin{array}{l}\text{Given Data,}\\ {\text{Q}}_{\text{1}}\text{ = +3}\\ {\text{Q}}_2\text{ = -3}\\ \text{Distance }\left(d\right)\text{ = 2}\text{.5pm}\end{array}$

$\begin{array}{l}\text{The force of attraction for the two given charges,}\\ F_d\propto \frac{3\times \left(-3\right)}{{\left(\text{2}\text{.5pm}\right)}^2}\\ =-1.44\end{array}$

$\begin{array}{l}\text{Given Data,}\\ {\text{Q}}_{\text{1}}\text{ = +3}\\ {\text{Q}}_2\text{ = -3}\\ \text{Distance }\left(d\right)\text{ = 3pm}\end{array}$

$\begin{array}{l}\text{The force of attraction for the two given charges,}\\ F_e\propto \frac{3\times \left(-3\right)}{{\left(\text{3pm}\right)}^2}\\ =-1\end{array}$

Examining all the other options and determining the force of attraction shows that they are not as strong as the correct option.

Therefore, the incorrect options are options a. b, d and e.

Conclusion

Conclusion

The correct option that provides strong force of attraction for given charges is determined by using the given formula.