Convert electronvolt to atomic unit of energy

Learn how to convert 1 electronvolt to atomic unit of energy step by step.

Calculation Breakdown

Set up the equation

1.0 (e l e c t r o n v o l t) = x (a t o m i c u n i t o f e n e r g y)

Define the base values of the selected units in relation to the SI unit

(j o u l e)

Left side: 1.0 (e l e c t r o n v o l t) = 1.602176462 \times 10^{- 19} (j o u l e) = 1.602176462 \times 10^{- 19} (J)

Right side: 1.0 (a t o m i c u n i t o f e n e r g y) = 4.359744 \times 10^{- 18} (j o u l e) = 4.359744 \times 10^{- 18} (J)

Insert known values into the conversion equation to determine

x

1.0 (e l e c t r o n v o l t) = x (a t o m i c u n i t o f e n e r g y)

Insert known values =>

1.0 \times 1.602176462 \times 10^{- 19} \times (j o u l e) = x \times 4.359744 \times 10^{- 18} \times (j o u l e)

Or

1.0 \cdot 1.602176462 \times 10^{- 19} \cdot (J) = x \cdot 4.359744 \times 10^{- 18} \cdot (J)

Cancel SI units

1.0 \times 1.602176462 \times 10^{- 19} \cdot (J) = x \times 4.359744 \times 10^{- 18} \times (J)

Conversion Equation

1.602176462 \times 10^{- 19} = x \times 4.359744 \times 10^{- 18}

Cancel factors on both sides

Cancel factors

1.602176462 \times {10^{- 19}}^{10^{- 1}} = x \times 4.359744 \times 10^{- 18}

Simplify

1.602176462 \times 10^{- 1} = x \times 4.359744

Switch sides

x \times 4.359744 = 1.602176462 \times 10^{- 1}

Isolate

x

Multiply both sides by

(\frac{1.0}{4.359744})

x \times 4.359744 \times \frac{1.0}{4.359744} = 1.602176462 \times 10^{- 1} \times \frac{1.0}{4.359744}

Cancel

x \times 4.359744 \times \frac{1.0}{4.359744} = 1.602176462 \times 10^{- 1} \times \frac{1.0}{4.359744}

Simplify

x = \frac{1.602176462 \times 10^{- 1}}{4.359744}

Solve

x

x \approx 0.0367493243 \approx 3.6749 \times 10^{- 2}

Conversion Equation

1.0 (e l e c t r o n v o l t) \approx 3.6749 \times 10^{- 2} (a t o m i c u n i t o f e n e r g y)

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