Convert rydberg to electronvolt
Learn how to convert
1
rydberg to
electronvolt
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(rydberg\right)={\color{rgb(20,165,174)} x}\left(electronvolt\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(joule\right)\)
\(\text{Left side: 1.0 } \left(rydberg\right) = {\color{rgb(89,182,91)} 2.179872 \times 10^{-18}\left(joule\right)} = {\color{rgb(89,182,91)} 2.179872 \times 10^{-18}\left(J\right)}\)
\(\text{Right side: 1.0 } \left(electronvolt\right) = {\color{rgb(125,164,120)} 1.602176462 \times 10^{-19}\left(joule\right)} = {\color{rgb(125,164,120)} 1.602176462 \times 10^{-19}\left(J\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(rydberg\right)={\color{rgb(20,165,174)} x}\left(electronvolt\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 2.179872 \times 10^{-18}} \times {\color{rgb(89,182,91)} \left(joule\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.602176462 \times 10^{-19}}} \times {\color{rgb(125,164,120)} \left(joule\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 2.179872 \times 10^{-18}} \cdot {\color{rgb(89,182,91)} \left(J\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.602176462 \times 10^{-19}} \cdot {\color{rgb(125,164,120)} \left(J\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 2.179872 \times 10^{-18}} \cdot {\color{rgb(89,182,91)} \cancel{\left(J\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.602176462 \times 10^{-19}} \times {\color{rgb(125,164,120)} \cancel{\left(J\right)}}\)
\(\text{Conversion Equation}\)
\(2.179872 \times 10^{-18} = {\color{rgb(20,165,174)} x} \times 1.602176462 \times 10^{-19}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(2.179872 \times {\color{rgb(255,204,153)} \cancel{10^{-18}}} = {\color{rgb(20,165,174)} x} \times 1.602176462 \times {\color{rgb(255,204,153)} \cancelto{10^{-1}}{10^{-19}}}\)
\(\text{Simplify}\)
\(2.179872 = {\color{rgb(20,165,174)} x} \times 1.602176462 \times 10^{-1}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 1.602176462 \times 10^{-1} = 2.179872\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{1.602176462 \times 10^{-1}}\right)\)
\({\color{rgb(20,165,174)} x} \times 1.602176462 \times 10^{-1} \times \dfrac{1.0}{1.602176462 \times 10^{-1}} = 2.179872 \times \dfrac{1.0}{1.602176462 \times 10^{-1}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1.602176462}} \times {\color{rgb(99,194,222)} \cancel{10^{-1}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1.602176462}} \times {\color{rgb(99,194,222)} \cancel{10^{-1}}}} = 2.179872 \times \dfrac{1.0}{1.602176462 \times 10^{-1}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{2.179872}{1.602176462 \times 10^{-1}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-1}}\text{ can be rewritten to }10\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10.0 \times 2.179872}{1.602176462}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx13.60569233\approx13.6057\)
\(\text{Conversion Equation}\)
\(1.0\left(rydberg\right)\approx{\color{rgb(20,165,174)} 13.6057}\left(electronvolt\right)\)
