Respuesta :
Explanation:
Formula for work done is as follows.
W = [tex]-k \frac{q_{1}q_{2}}{d}[/tex]
where, k = proportionality constant = [tex]8.99 \times 10^{9} Jm/C^{2}[/tex]
[tex]q_{1} = charge of Mg^{2+} = 3.2 \times 10^{-19} C[/tex]
[tex]q_{2} = charge of O_{2-} = -3.2 \times 10^{-19} C[/tex]
d = separation distance = 0.45 nm = [tex]0.45 \times 10^{-9} m[/tex]
Now, we will put the given values into the above formula and calculate work done as follows.
W = [tex]-k \frac{q_{1}q_{2}}{d}[/tex]
= [tex]\frac{-[8.99 \times 10^{9} Jm/C^{2} \times 3.2 \times 10^{-19} C \times -3.2 \times 10^{-19} C]}{0.25 \times 10^{-9} m}[/tex]
= [tex]3.68 \times 10^{-18} J[/tex]
Thus, we can conclude that work required to increase the separation of the two ions to an infinite distance is [tex]3.68 \times 10^{-18} J
[/tex].
The amount of work required to increase the separation of the two ions to an infinite distance is [tex]3.68[/tex] × [tex]10^{-18}\;Joules[/tex].
Given the following data:
- Quantity of [tex]Mg^{2+}[/tex] = [tex]3.2[/tex] × [tex]10^{-19}\;C[/tex]
- Quantity of [tex]O^{2-}[/tex] = [tex]-3.2[/tex] × [tex]10^{-19}\;C[/tex]
- Distance = 0.25 nm = [tex]0.25[/tex] × [tex]10^{-9}\;m[/tex]
We know that the constant of proportionality is equal to [tex]8.99[/tex] × [tex]10^{9}\; Jm/C^2[/tex]
To find how much work would be required to increase the separation of the two ions to an infinite distance:
Mathematically, the work done in separating two charges is given by the formula:
[tex]Work =-k \frac{q_1q_2}{d}[/tex]
Where:
- d is the distance between two charges.
- [tex]q_1 \;and \;q_2[/tex] are the two charges respectively.
- k is the constant of proportionality.
Substituting the values into the formula, we have:
[tex]Work =-8.99(10^{9}) \frac{[3.2(10^{-19})(-3.2(10^{-19})}{0.25(10^{-9})}\\\\Work = -8.99(10^{9}) \frac{-1.024(10^{-37})}{0.25(10^{-9})}\\\\Work = \frac{9.21(10^{-28})}{0.25(10^{-9})}[/tex]
Work = [tex]3.68[/tex] × [tex]10^{-18}\;Joules[/tex]
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