Using values from Table 7.1, how many DNA molecules could be broken by the energy carried by a single electron in the beam of an old-fashioned TV tube? (These electrons were not dangerous in themselves, but they did create dangerous x rays. Later model tube TVs had shielding that absorbed x rays before they escaped and exposed viewers.)

Conservation of energy:The total energy of an isolated system is always conserved. In other words, the energy neither be created nor be destroyed; it can be only transformed from one form to another.

When a single electron in the beam of an old-fashioned TV tube strikes on the molecules of DNA, the total energy of the single electron will break many molecules of DNA. Mathematically,

$E_{electron}=n{E}_{DNA}$

Here,$E_{electron}$is the energy of single electron in the beam of old-fashioned TV tube$\left(E_{electron}=4.0\times {10}^{-15}\text{J}\right)$, n is number of molecules of DNA broken, and$E_{DNA}$is the energy required to break one DNA molecule$\left(E_{DNA}={10}^{-19}\text{J}\right)$.

The expression for the number of molecules of DNA broken is,

$n=\frac{E_{electron}}{E_{DNA}}$

Putting all known values,

$$\begin{gathered} n=\frac{4.0\times {10}^{-15}\text{J}}{{10}^{-19}\text{J}} \\ =40000 \end{gathered}$$

Therefore, a single electron in the beam of anold-fashioned TV tube can break$40000$ molecules of DNA.