Video: Finding the Ratio of Two Quantities of Energy in a Real-World Context

10⁻¹⁹ J of energy are required to break one DNA strand. How many DNA molecules could be broken by the energy carried by a single electron in the beam of an old-fashioned TV tube that carries 4 × 10⁻¹⁵ J of energy?

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Video Transcript

10 to the negative 19th joules of energy are required to break one DNA strand. How many DNA molecules could be broken by the energy carried by a single electron in the beam of an old-fashioned TV tube that carries four times 10 to the negative 15th joules of energy?

In this statement, we’re told that it takes 10 to the negative 19 joules of energy to break a DNA strand; we’ll call that 𝐸 sub 𝑏. We’re then told that the electron energy in an old TV tube is four times 10 to the negative 15th joules; we’ll call that 𝐸 sub 𝑒 for the energy of a single electron.

We want to know how many DNA molecules could be broken by 𝐸 sub 𝑒; we’ll call that number capital 𝑁. 𝑁 will be equal to the electron energy divided by the energy required to break a DNA strand. This means that 𝑁 equals 𝐸 sub 𝑒 divided by 𝐸 sub 𝑏. This equals 10 to the negative 10th [19th] joules divided by four times 10 to the negative 15th joules. This equals 10 to the negative 19th joules divided by four times 10 to the negative 15th joules.

Entering these values on our calculator and keeping one significant figure, 𝑁 is equal to four times 10 to the fourth. This is 40000, the number of DNA molecules that could be broken by the energy in a single electron in an old TV tube.

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