Convert Elementary Charge to electrostatic unit of charge
Learn how to convert
1
Elementary Charge to
electrostatic unit of charge
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(Elementary \text{ } Charge\right)={\color{rgb(20,165,174)} x}\left(electrostatic \text{ } unit \text{ } of \text{ } charge\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(coulomb\right)\)
\(\text{Left side: 1.0 } \left(Elementary \text{ } Charge\right) = {\color{rgb(89,182,91)} 1.602176487 \times 10^{-19}\left(coulomb\right)} = {\color{rgb(89,182,91)} 1.602176487 \times 10^{-19}\left(C\right)}\)
\(\text{Right side: 1.0 } \left(electrostatic \text{ } unit \text{ } of \text{ } charge\right) = {\color{rgb(125,164,120)} 3.33564 \times 10^{-10}\left(coulomb\right)} = {\color{rgb(125,164,120)} 3.33564 \times 10^{-10}\left(C\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(Elementary \text{ } Charge\right)={\color{rgb(20,165,174)} x}\left(electrostatic \text{ } unit \text{ } of \text{ } charge\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 1.602176487 \times 10^{-19}} \times {\color{rgb(89,182,91)} \left(coulomb\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 3.33564 \times 10^{-10}}} \times {\color{rgb(125,164,120)} \left(coulomb\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 1.602176487 \times 10^{-19}} \cdot {\color{rgb(89,182,91)} \left(C\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 3.33564 \times 10^{-10}} \cdot {\color{rgb(125,164,120)} \left(C\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 1.602176487 \times 10^{-19}} \cdot {\color{rgb(89,182,91)} \cancel{\left(C\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 3.33564 \times 10^{-10}} \times {\color{rgb(125,164,120)} \cancel{\left(C\right)}}\)
\(\text{Conversion Equation}\)
\(1.602176487 \times 10^{-19} = {\color{rgb(20,165,174)} x} \times 3.33564 \times 10^{-10}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(1.602176487 \times {\color{rgb(255,204,153)} \cancelto{10^{-9}}{10^{-19}}} = {\color{rgb(20,165,174)} x} \times 3.33564 \times {\color{rgb(255,204,153)} \cancel{10^{-10}}}\)
\(\text{Simplify}\)
\(1.602176487 \times 10^{-9} = {\color{rgb(20,165,174)} x} \times 3.33564\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 3.33564 = 1.602176487 \times 10^{-9}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{3.33564}\right)\)
\({\color{rgb(20,165,174)} x} \times 3.33564 \times \dfrac{1.0}{3.33564} = 1.602176487 \times 10^{-9} \times \dfrac{1.0}{3.33564}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{3.33564}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{3.33564}}} = 1.602176487 \times 10^{-9} \times \dfrac{1.0}{3.33564}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.602176487 \times 10^{-9}}{3.33564}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0000000005\approx4.8032 \times 10^{-10}\)
\(\text{Conversion Equation}\)
\(1.0\left(Elementary \text{ } Charge\right)\approx{\color{rgb(20,165,174)} 4.8032 \times 10^{-10}}\left(electrostatic \text{ } unit \text{ } of \text{ } charge\right)\)
