Convert atomic unit of energy to cubic meter of atmosphere
Learn how to convert
1
atomic unit of energy to
cubic meter of atmosphere
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(atomic \text{ } unit \text{ } of \text{ } energy\right)={\color{rgb(20,165,174)} x}\left(cubic \text{ } meter \text{ } of \text{ } atmosphere\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(joule\right)\)
\(\text{Left side: 1.0 } \left(atomic \text{ } unit \text{ } of \text{ } energy\right) = {\color{rgb(89,182,91)} 4.359744 \times 10^{-18}\left(joule\right)} = {\color{rgb(89,182,91)} 4.359744 \times 10^{-18}\left(J\right)}\)
\(\text{Right side: 1.0 } \left(cubic \text{ } meter \text{ } of \text{ } atmosphere\right) = {\color{rgb(125,164,120)} 1.01325 \times 10^{-4}\left(joule\right)} = {\color{rgb(125,164,120)} 1.01325 \times 10^{-4}\left(J\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(atomic \text{ } unit \text{ } of \text{ } energy\right)={\color{rgb(20,165,174)} x}\left(cubic \text{ } meter \text{ } of \text{ } atmosphere\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 4.359744 \times 10^{-18}} \times {\color{rgb(89,182,91)} \left(joule\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.01325 \times 10^{-4}}} \times {\color{rgb(125,164,120)} \left(joule\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 4.359744 \times 10^{-18}} \cdot {\color{rgb(89,182,91)} \left(J\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.01325 \times 10^{-4}} \cdot {\color{rgb(125,164,120)} \left(J\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 4.359744 \times 10^{-18}} \cdot {\color{rgb(89,182,91)} \cancel{\left(J\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.01325 \times 10^{-4}} \times {\color{rgb(125,164,120)} \cancel{\left(J\right)}}\)
\(\text{Conversion Equation}\)
\(4.359744 \times 10^{-18} = {\color{rgb(20,165,174)} x} \times 1.01325 \times 10^{-4}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(4.359744 \times {\color{rgb(255,204,153)} \cancelto{10^{-14}}{10^{-18}}} = {\color{rgb(20,165,174)} x} \times 1.01325 \times {\color{rgb(255,204,153)} \cancel{10^{-4}}}\)
\(\text{Simplify}\)
\(4.359744 \times 10^{-14} = {\color{rgb(20,165,174)} x} \times 1.01325\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 1.01325 = 4.359744 \times 10^{-14}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{1.01325}\right)\)
\({\color{rgb(20,165,174)} x} \times 1.01325 \times \dfrac{1.0}{1.01325} = 4.359744 \times 10^{-14} \times \dfrac{1.0}{1.01325}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1.01325}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1.01325}}} = 4.359744 \times 10^{-14} \times \dfrac{1.0}{1.01325}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{4.359744 \times 10^{-14}}{1.01325}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx4.3027327905 \times 10^{-14}\approx4.3027 \times 10^{-14}\)
\(\text{Conversion Equation}\)
\(1.0\left(atomic \text{ } unit \text{ } of \text{ } energy\right)\approx{\color{rgb(20,165,174)} 4.3027 \times 10^{-14}}\left(cubic \text{ } meter \text{ } of \text{ } atmosphere\right)\)
