Convert electronvolt to rydberg
Learn how to convert
1
electronvolt to
rydberg
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(electronvolt\right)={\color{rgb(20,165,174)} x}\left(rydberg\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(joule\right)\)
\(\text{Left side: 1.0 } \left(electronvolt\right) = {\color{rgb(89,182,91)} 1.602176462 \times 10^{-19}\left(joule\right)} = {\color{rgb(89,182,91)} 1.602176462 \times 10^{-19}\left(J\right)}\)
\(\text{Right side: 1.0 } \left(rydberg\right) = {\color{rgb(125,164,120)} 2.179872 \times 10^{-18}\left(joule\right)} = {\color{rgb(125,164,120)} 2.179872 \times 10^{-18}\left(J\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(electronvolt\right)={\color{rgb(20,165,174)} x}\left(rydberg\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 1.602176462 \times 10^{-19}} \times {\color{rgb(89,182,91)} \left(joule\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.179872 \times 10^{-18}}} \times {\color{rgb(125,164,120)} \left(joule\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 1.602176462 \times 10^{-19}} \cdot {\color{rgb(89,182,91)} \left(J\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.179872 \times 10^{-18}} \cdot {\color{rgb(125,164,120)} \left(J\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 1.602176462 \times 10^{-19}} \cdot {\color{rgb(89,182,91)} \cancel{\left(J\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 2.179872 \times 10^{-18}} \times {\color{rgb(125,164,120)} \cancel{\left(J\right)}}\)
\(\text{Conversion Equation}\)
\(1.602176462 \times 10^{-19} = {\color{rgb(20,165,174)} x} \times 2.179872 \times 10^{-18}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(1.602176462 \times {\color{rgb(255,204,153)} \cancelto{10^{-1}}{10^{-19}}} = {\color{rgb(20,165,174)} x} \times 2.179872 \times {\color{rgb(255,204,153)} \cancel{10^{-18}}}\)
\(\text{Simplify}\)
\(1.602176462 \times 10^{-1} = {\color{rgb(20,165,174)} x} \times 2.179872\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 2.179872 = 1.602176462 \times 10^{-1}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{2.179872}\right)\)
\({\color{rgb(20,165,174)} x} \times 2.179872 \times \dfrac{1.0}{2.179872} = 1.602176462 \times 10^{-1} \times \dfrac{1.0}{2.179872}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{2.179872}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{2.179872}}} = 1.602176462 \times 10^{-1} \times \dfrac{1.0}{2.179872}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.602176462 \times 10^{-1}}{2.179872}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0734986486\approx7.3499 \times 10^{-2}\)
\(\text{Conversion Equation}\)
\(1.0\left(electronvolt\right)\approx{\color{rgb(20,165,174)} 7.3499 \times 10^{-2}}\left(rydberg\right)\)
