The energy of one mole of photons of a specific electromagnetic radiation is 200 kJ mol ⁻¹ . The frequency of this radiation is x 10¹⁴ Hz . The value of x is _____. (Nearest integer) (Given: h = 6.626 10⁻³⁴ J s , N_A = 6.022 10²³ mol ⁻¹ )

Step-by-step solution

Energy of one mole of photons, E_ mole = 200 kJ mol ⁻¹ = 200000 J mol ⁻¹ . The energy of a single photon is given by: E_ photon = E_ mole N_A According to Planck's quantum theory, the energy of a photon is also given by: E_ photon = h Equating the two expressions for the energy of a single photon: h = E_ mole N_A = E_ mole N_A h = 200000 6.022 10²³ 6.626 10⁻³⁴ = 200000 39.90 10⁻¹¹ = 5.012 10¹⁴ Hz Comparing this with x 10¹⁴ Hz , we get x 5 . Answer: 5