QuestionConvert $1.5 \times 10^{9}$ eV to calories.

Studdy Solution

STEP 1

Assumptions1. The energy value given is $1.5 \times10^{9}$ electron-volts (eV). . We need to convert this energy value to calories.
3. The conversion factors are as follows -1 eV = $1.602 \times10^{-19}$ joules (J) -1 cal =4.184 J

STEP 2

First, we need to convert the energy value from electron-volts to joules. We can do this by multiplying the energy value by the conversion factor.
$Energy_{J} = Energy_{eV} \\times Conversion\, factor_{eV\, to\, J}$

STEP 3

Now, plug in the given values for the energy value and the conversion factor to calculate the energy in joules.
$Energy_{J} =1.5 \times10^{9}\, eV \\times1.602 \times10^{-19}\, J/eV$

STEP 4

Calculate the energy amount in joules.
$Energy_{J} =1. \times10^{9} \\times1.602 \times10^{-19} =0.2403\, J$

STEP 5

Now that we have the energy amount in joules, we can convert this to calories. We can do this by dividing the energy value by the conversion factor.
$Energy_{cal} = Energy_{J} / Conversion\, factor_{J\, to\, cal}$

STEP 6

Plug in the values for the energy amount in joules and the conversion factor to calculate the energy in calories.
$Energy_{cal} =0.2403\, J /4.184\, J/cal$

STEP 7

Calculate the energy amount in calories.
$Energy_{cal} =0.2403 /4.184 =0.0574\, cal$ The energy of $1.5 \times10^{9}$ electron-volts is equivalent to0.0574 calories.

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