Question

A mole of red photons of wavelength 725 nm has ________ kJ of energy. 7/5 a. 6.05 x 10−3 b. 2.74 x 10−19 c. 4.56 x 10−19 d. 227 e. 165

Answer 1

Answer: 165.1kJ

Explanation:

The energy of a photon of wavelength 725nm can be written as:

E = hv = hc/λ .....1

since v = c/λ

Where:

λ = wavelength of photon = 725nm = 725 × 10^-9m

h = Planck's constant = 6.626 × 10^-34 Js

c = speed of light = 3.0 × 10^8 m/s

v = frequency

E = energy of the photon

Substituting the values into equation 1, we have:

E = 6.626×3/725 × 10^(-34+8+9) J

E = 0.02742 × 10^-17 J

E = 2.742 × 10^-19 J

Therefore, for one mole of red photons, according to Avogadro's constant:

1 mole = 6.022 × 10^23 photons

So, the total energy of 1 mole of photons is:

E(total) = 2.742 × 10^-19 J × 6.022 × 10^23 photons

E(total) = 16.51 × 10^4 J = 165.1kJ

Therefore, A mole of red photons of wavelength 725 nm has 165.1 kJ of energy.