Question

A recent study found that electrons that have energies between 3.45 eV and 19.9 eV can cause breaks in a DNA molecule even though they do not ionize the molecule. If a single photon were to transfer its energy to a single electron, what range of light wavelengths could cause DNA breaks?minimum wavelength?
maximum wavelength?

Answer 1

Answer:

The Minimum wavelength is  $\lambda_{min}= 382.2nm$

The Maximum wavelength is $\lambda_{max}= 624.2nm$

Explanation:

From the question we are told that  

              The energy range is  $E_r = 3.25eV \ and \ 19.9eV$

   Considering $E = 19.9eV$

When a single photon is transferred to to an electron the energy obtained can be calculated as follows

              $E = 19.9eV = 19.9 *1.6 *10^{-19}J$

This energy is mathematically represented as

                    $E = \frac{hc}{\lambda_{max}}$

Here h is the Planck's constant with value of  $h= 6.625*10^{-34}J\cdot s$

        c is the speed of light with value of  $c = 3*10^8 m/s$

Substituting values and making $\lambda$ the subject of the formula

                       $\lambda_{max} = \frac{hc}{E}$

                         $= \frac{6.625*10^{-34} * 3.0*10^{8}}{19.9*1.6*10^{-19}}$

                         $\lambda_{max}= 624.2nm$

  Considering $E = 3.25eV$

When a single photon is transferred to to an electron the energy obtained can be calculated as follows

              $E = 19.9eV = 3.25 *1.6 *10^{-19}J$

This energy is mathematically represented as

                    $E = \frac{hc}{\lambda_{min}}$

Substituting values and making $\lambda$ the subject of the formula

                       $\lambda_{min} = \frac{hc}{E}$

                           $= \frac{6.625*10^{-34} * 3.0*10^{8}}{3.25*1.6*10^{-19}}$

                           $\lambda_{min}= 382.2nm$