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

Answer:

5.95 nm to 33.6 nm

Explanation:

Energy of a single photon can be written as:

$E = \frac{hc}{\lambda}$

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

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

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

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