Question

A recent study found that electrons that have energies between 3.45 eV and 20.9 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?

Answer 1

5.95 nm to 33.6 nm

Step-by-step explanation:

Energy of a single photon can be written as:

`E = (hc)/(\lambda)`

where, h is the Planck's constant, c is the speed of light and λ is the wavelength of light.

Consider the lowest energy of an electron that can break a DNA = 3.45 eV

1 eV = 1.6 ×10⁻¹⁹ J

⇒3.45 eV = 5.52×10⁻¹⁹ J

`E = (hc)/(\lambda)\\ \Rightarrow \lambda = (hc)/(E)= \frac {6.63* 10^(-34) m^2kg/s * 3* 10^8 m/s}{5.52 * 10^(-19) J} = 3.60* 10^(-7) m = 360 nm`

Consider the highest energy of an electron that can break a DNA = 20.9 eV

1 eV = 1.6 ×10⁻¹⁹ J

⇒20.9 eV = 33.4×10⁻¹⁹ J

`E = (hc)/(\lambda)\\ \Rightarrow \lambda = (hc)/(E)= \frac {6.63* 10^(-34) m^2kg/s * 3* 10^8 m/s}{33.4 * 10^(-19) J} = 0.595* 10^(-7) m = 59.5 nm`