Question

A certain dye absorbs light of certain wavelength and then flouresence light of wavelength 5000 angstrom assuming that under given conditions, 50% of the absorbed energy is re emitted out in the form of floroscence and the ratio of number of quanta emitted out to the number of quanta absorbed is 5:8,find the wavelength of absorbed (in angstrom)

Answer 1

Answer:

The wavelength of absorbed light is 8000 angstrom.

Explanation:

Wavelength of the florescence light = $5000 \AA$

Energy associated with with 1 photon of this light:

$E=\frac{hc}{\lambda }$

$E=\frac{hc}{5000\times 10^{-10} m}$

Let the number of photons or quanta emitted be x.

Let the number of photons or quanta absorbed be y.

Total energy emitted $E'=xE$

The ratio of number of quanta emitted out to the number of quanta absorbed is 5:8.

$\frac{x}{y}=\frac{5}{8}$

y=$\frac{8}{5}x$

Total energy absorbed = E''

$50\%=\frac{E'}{E''}\times 100$

$E''=\frac{x\times E}{50}\times 100$

$E''= y\times E_o$

$y\times E_o=x\times E\times 2$

$E_o$ = energy of a photon absorbed

$\frac{8}{5}x\times \frac{hc}{\lambda '}=x\times E\times 2\times \frac{hc}{5000\times 10^{-10} m}$

$\lambda '=8000\times 10^{-10}m=8000\AA$

The wavelength of absorbed light is 8000 angstrom.