Question

An atom is in its excited state. Does the probability of its coming to ground state depend on whether the radiation is already present or not? If yes, does it also depend on the wavelength of the radiation present?

Answer 1

When an atom transits from an excited state to ground state in the presence of an external radiation then it is called as stimulated transition.
When an atom transits from an excited state to ground state on its own then it is called as spontaneous transition.
Ratio of the coefficient for stimulated transition to spontaneous transition is given by
$R=\frac{A}{B\rho \left(\nu \right)}=e^{\frac{h\nu }{kT}}-1$
For microwave region
$$\begin{gathered} \nu ={10}^{10}\left(\mathrm{say}\right) \\ \mathrm{R}={\mathrm{e}}^{\frac{6.6\times {10}^{-34}\times {10}^{10}}{1.38\times {10}^{-23}\times 300}}-1 \\ ={\mathrm{e}}^{0.0016}-1 \\ =0.0016 \end{gathered}$$
This implies that stimulated transition dominate in this region.
For visible region
$$\begin{gathered} \nu ={10}^{15} \\ \Rightarrow R=e^{160}-1 \\ \Rightarrow R>>1 \end{gathered}$$
So here spontaneous transition dominate.