A certain spectral line has a wavelength of 4000 A o . Calculate the frequency and energy of the photons associated with it. e = 1 . 6 × 10 - 19 C , h = 6 . 63 × 10 - 34 Js

Given the wavelength of line λ = 4000 × 10 - 10 m e = 1 . 6 × 10 - 19 C , h = 6 . 63 × 10 - 34 Js The frequency of the radiation is given by ν = c λ where c , λ are the velocity and wave length of the light. Putting these values we have the frequency of the spectral line = 3 × 10 8 4000 × 10 - 10 = 0 . 75 × 10 15 H z The energy of a photon is given by the Planck's relation E = hν where ν = frequency of the radiation and h = Planck's constant Substituting the values in the formula, we have E = 6 . 63 × 10 - 34 × 0 . 75 × 10 15 1 . 6 × 10 - 19 = 3 . 1 eV

The energy of 6000 A o photon is 3 . 30 × 10 - 19 J . Find the energy of 4000 A o . e = 1 . 6 × 10 - 19 C , h = 6 . 63 × 10 - 34 Js

Given energy of photon E = 3 . 3 × 10 - 10 J . Wavelength of light λ = 6000 × 10 - 10 m The energy of a photon is given by Planck's relation E = hν = hc λ Where ν , c a n d λ are the frequency, speed and wave length of light. It indicates that E ∝ 1 λ Therefore, we have energy of photone 4000 ° A = 6000 × energy of 6000 ° A 4000 = 3 . 3 × 10 - 19 × 1 . 5 = 4 . 95 × 10 - 19 J .

5 % energy of a monochromatic light source is converted into light of wavelength 5600 A o . If the power of the source be 100 W , then how many photons of light will be emitted by it per second?

Given power of the source W = 100 W The wavelength og light = λ = 5600 × 10 - 10 m As power= energy per sec. = no . of photons × energy of each photon E = power no . ofphotons = 100 n As only 5 % is converted into the photons of wavelength 5600 ° A whose frequency is ν ' = c λ = 3 × 10 8 5600 × 10 - 7 = 5 . 357 × 10 14 H z As we require energy = hν ' = 5 n or n = 5 hv ' = 5 6 . 63 × 10 - 34 × 3 . 57 × 10 14 = 1 . 14 × 10 19 Hence the number of photons per sec= 1 . 14 × 10 19