Question

For an emission of wavelength 5000 Angstrom, at what temperatures both spontaneous and stimulated emissions will be same?

Answer 1

For an emission of wavelength 5000 Angstrom, both spontaneous and stimulated emissions will be same at temperature 28869.6 K

The Temperature is calculated by the formula

$\frac{N}{n}$=$e^{-hc/λKT}$-1

here, n is number of spontaneous emission, N number of stimulated emission, h is Planck's constant,  c is speed of light, K is Boltzmann constant, and T is temperature

Plugging the values in the above equation

1=$e^{-6.64*10^(-34)*3*10^8/(5000*10^(-10)*1.38*10^(-23)*T}$-1

T=28869.6 K