Convert rutherford to curie
Learn how to convert
1
rutherford to
curie
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(rutherford\right)={\color{rgb(20,165,174)} x}\left(curie\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(becquerel\right)\)
\(\text{Left side: 1.0 } \left(rutherford\right) = {\color{rgb(89,182,91)} 10^{6}\left(becquerel\right)} = {\color{rgb(89,182,91)} 10^{6}\left(Bq\right)}\)
\(\text{Right side: 1.0 } \left(curie\right) = {\color{rgb(125,164,120)} 3.7 \times 10^{10}\left(becquerel\right)} = {\color{rgb(125,164,120)} 3.7 \times 10^{10}\left(Bq\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(rutherford\right)={\color{rgb(20,165,174)} x}\left(curie\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{6}} \times {\color{rgb(89,182,91)} \left(becquerel\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 3.7 \times 10^{10}}} \times {\color{rgb(125,164,120)} \left(becquerel\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 10^{6}} \cdot {\color{rgb(89,182,91)} \left(Bq\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 3.7 \times 10^{10}} \cdot {\color{rgb(125,164,120)} \left(Bq\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{6}} \cdot {\color{rgb(89,182,91)} \cancel{\left(Bq\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 3.7 \times 10^{10}} \times {\color{rgb(125,164,120)} \cancel{\left(Bq\right)}}\)
\(\text{Conversion Equation}\)
\(10^{6} = {\color{rgb(20,165,174)} x} \times 3.7 \times 10^{10}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\({\color{rgb(255,204,153)} \cancel{10^{6}}} = {\color{rgb(20,165,174)} x} \times 3.7 \times {\color{rgb(255,204,153)} \cancelto{10^{4}}{10^{10}}}\)
\(\text{Simplify}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times 3.7 \times 10^{4}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 3.7 \times 10^{4} = 1.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{3.7 \times 10^{4}}\right)\)
\({\color{rgb(20,165,174)} x} \times 3.7 \times 10^{4} \times \dfrac{1.0}{3.7 \times 10^{4}} = \times \dfrac{1.0}{3.7 \times 10^{4}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{3.7}} \times {\color{rgb(99,194,222)} \cancel{10^{4}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{3.7}} \times {\color{rgb(99,194,222)} \cancel{10^{4}}}} = \dfrac{1.0}{3.7 \times 10^{4}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.0}{3.7 \times 10^{4}}\)
Rewrite equation
\(\dfrac{1.0}{10^{4}}\text{ can be rewritten to }10^{-4}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-4}}{3.7}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.000027027\approx2.7027 \times 10^{-5}\)
\(\text{Conversion Equation}\)
\(1.0\left(rutherford\right)\approx{\color{rgb(20,165,174)} 2.7027 \times 10^{-5}}\left(curie\right)\)
