# Question Video: Choosing the Correct Conversion Factor between Joules and Mega-Electron Volts Chemistry

Which of the following relations is correct? [A] To convert an amount of energy from joules to mega-electron volts, we divide it by 1.6 × 10⁻²⁷. [B] To convert an amount of energy from joules to mega-electron volts, we divide it by 1.6 × 10⁻¹³. [C] To convert an amount of energy from joules to mega-electron volts, we multiply it by 1.6 × 10⁻²⁷. [D] To convert an amount of energy from joules to mega-electron volts, we multiply it by 1.6 × 10⁻¹³.

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### Video Transcript

Which of the following relations is correct? (A) To convert an amount of energy from joules to mega-electron volts, we divide it by 1.6 times 10 to the negative 27. (B) To convert an amount of energy from joules to mega-electron volts, we divide it by 1.6 times 10 to the negative 13. (C) To convert an amount of energy from joules to mega-electron volts, we multiply it by 1.6 times 10 to the negative 27. (D) To convert an amount of energy from joules to mega-electron volts, we multiply it by 1.6 times 10 to the negative 13.

An electron volt is the amount of energy gained by an electron when it travels through a potential of one volt. This unit of energy is commonly used for energy changes in atomic processes. For example, removing the electron from a hydrogen atom requires 13.6 electron volts of energy. Breaking apart the helium nucleus into protons and neutrons requires 28.3 mega-electron volts of energy. Mega-electron volts are the subject of this question. We need to determine the relationship between mega-electron volts and joules.

There are one million electron volts in a mega-electron volt. We can also express one million as 10 to the sixth. So we can convert from mega-electron volts to electron volts if we multiply by 10 raised to the power of six. One electron volt is equivalent to 1.602 times 10 to the negative 19 joules. So we can convert from electron volts to joules if we multiply by this number. The combination of these two conversions gives us 1.602 times 10 to the negative 13 joules, which we’ll round to one decimal place to match the answer choices. So one mega-electron volt is equal to 1.6 times 10 to the negative 13 joules.

We can rule out answer choices (A) and (C) as our conversion factor is not 1.6 times 10 to the negative 27. Now we need to know if we should divide or multiply by this number. So if we had some amount of energy in joules and we want to convert it into mega-electron volts, we would divide by our conversion factor. We can see this way that the units of joules cancel, leaving us in the correct units of mega-electron volts. So of the relations in this problem, answer choice (B) was correct. To convert an amount of energy from joules to mega-electron volts, we divide it by 1.6 times 10 to the negative 13.