Question

(a) The first step in ozone formation in the upper atmosphere occurs when oxygen molecules absorb UV radiation of wavelengths ≤ 242 nm. Calculate the frequency and energy of the least energetic of these photons. (b) Ozone absorbs light having wavelengths of 2200 to 2900 Å, thus protecting organisms on Earth’s surface from this high-energy UV radiation. What are the frequency and energy of the most energetic of these photons?

Answer 1

Answer:

a) f = (1.24 × 10^15) Hz and E = (8.214 × 10^-19) J

b) f = (1.36 × 10^15) Hz; E = (9.035 × 10^-19) J

Explanation:

a) The least energetic photons have the highest wavelength. That is, the wavelength of the least energetic photons is equal to the upperlimit of the wavelength inequality given.

λ = 242nm = 2.42 × 10⁻7 m

v = fλ; f = v/λ; v = 3×10^8 m/s

f = (3×10^8)/(2.42×10^-7)

f = (1.24 × 10^15) Hz

E = hf; h = planck's constant = (6.62607004 × 10^-34) Js

E = 6.626 × 10^-34 × 1.24 × 10^15

E = (8.214 × 10^-19) J

b) The photons with the least wavelength in the range provided are the most energetic ones.

λ = (2200 × 10^-10) m = (2.2 × 10^-7) m

v = fλ; f = v/λ; v = 3×10^8 m/s

f = (3×10^8)/(2.2×10^-7)

f = (1.36 × 10^15) Hz

E = hf; h = planck's constant = (6.62607004 × 10^-34) Js

E = 6.626 × 10^-34 × 1.36 × 10^15

E = (9.035 × 10^-19) J

QED!