Question

Mercury vapor emits lights as several wavelengths, but the primary ones are 365.4 nm, 404.7 nm, and 435.8 nm. Assuming all the energy from a 100 W bulb is released equally across these three wavelengths, how many photons per second are emitted for each wavelength, and what is the energy of individual photons (in J and kJ/mol) for each wavelength?

Answer 1

E = 100 W = 100 J/s

now,

From wavlength

E= h c / WL

h = Planck Constant = 6.626*10^-34 J s

c = speed of particle (i.e. light) = 3*10^8 m/s

E = energy per particle J/photon

WL = wavelength in meters

E= (6.626*10^-34)(3*10^8)/(WL*10^-9)

E(365.4 nm) = (6.626*10^-34)(3*10^8)/(365.4*10^-9) =5.44*10^-19 J/photon

E(404.7 nm) = (6.626*10^-34)(3*10^8)/(404.7 *10^-9) =4.91*10^-19 J/photon

E(435.8 nm) = (6.626*10^-34)(3*10^8)/(435.8 *10^-9) =4.56*10^-19 J/photon

for kJ/mol photon:

E(365.4 nm) = (5.44*10^-19)(6.022*10^23)/(1000) = 327.5968 kJ/mol

E(404.7 nm) =(4.91*10^-19)((6.022*10^23)/(1000)) = 295.6802kJ

E(435.8 nm) =(4.56*10^-19)((6.022*10^23)/(1000)) = 274.60 kJ

No photons = Etotal/Eper photon

No (365.4 nm) photons = Etotal/Eper photon = 100/(5.44*10^-19) = 1.838*10^20 photons/s

No (404.7 nm) photons = Etotal/Eper photon = 100/(4.91*10^-19)= 2.036*10^20 photons/s

No (435.8 nm) photons = Etotal/Eper photon = 100/(4.56*10^-19) = 2.1929*10^20 photons/s