Question

Excessive exposure to ultraviolet radiation can damage skin cells' DNA and lead to skin cancer. Calculate the number of ultraviolet photons with a 350nm wavelength that account for 1.5 J of energy.

a) 4.72 x 10^18 photons
b) 2.14 x 10^16 photons
c) 1.42 x 10^20 photons
d) 2.6 x 10ˆ18 photons

Answer 1

The answer is approximately 2.6 x 10^18 photons.

Step-by-step explanation:

The student's question involves calculating the number of ultraviolet (UV) photons that amount to 1.5 Joules of energy, given a wavelength of 350 nm. To solve this, we use the energy equation for photons: E = hf, where E is the energy of one photon, h is Planck's constant (6.626 x 10-34 J·s), and f is the frequency of the radiation. First, we calculate the frequency using the wave equation f = c/λ, where c is the speed of light (3 x 108 m/s), and λ (lambda) is the wavelength. After finding the frequency, we can determine the energy of one photon and then the total number of photons by dividing the total energy (1.5 J) by the energy of one photon.

Calculating step by step:

• Find the frequency: f = c/λ = (3 x 108 m/s) / (350 x 10-9 m) = 8.57 x 1014 Hz
• Calculate the energy of one photon: E = hf = (6.626 x 10-34 J·s) x (8.57 x 1014 Hz) = 5.68 x 10-19 J
• Finally, determine the total number of photons: number of photons = total energy / energy of one photon = 1.5 J / 5.68 x 10-19 J/photon ≈ 2.64 x 1018 photons

Thus, the correct answer to the student's question is (d) 2.6 x 1018 photons.