Question

Summer is coming and we are ready to get out and get in the sun. However, sun light has some ultraviolet light. When a UV photon is absorbed by a molecule of DNA, there are different ways the energy can be absorbed. One of the ways is that the energy of the photon can be converted into vibrational energy of the molecular bonds. Excessive vibration can damage the molecule by causing the bonds to break. UV light of less than 290 nm causes significant damage to DNA and UV light of longer wavelength causes minimal damage. What is the threshold photon energy, in eV, for DNA damage

Answer 1

The threshold photon energy for DNA damage = 4.28 eV

Step-by-step explanation:

According to the Planck - Einstein's equation, the energy of a photon, E is proportional to its frequency; E = hf where f is frequency and h is Planck's constant.

Also, frequency, f = velocity /wavelength

f = c/λ where c is the velocity of light

E = hc/λ

h = 6.63 × 10^-³⁴ Js;

c = 3.0 × 10⁸ m/s;

Threshold wavelength, λ = 290 nm = 2.9 × 10^-7 m

E = (6.63 × 10^-³⁴ × 3.0 × 10⁸) / 2.9 × 10^-⁷

E = 6.85 × 10^-¹⁹ J

1 ev = 1.602 × 10^-¹⁹ J

6.85 × 10^-¹⁹ J = 6.85 × 10^-¹⁹ J × 1 eV / 1.602 × 10^-¹⁹ J = 4.28 eV

Therefore, the threshold photon energy for DNA damage = 4.28 eV