Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r = $${{\lambda _1}}$$/$${{\lambda _2}}$$, is given by:

A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At sometime t, the ratio of the number of B to that of A is 0.3. Then, t is given by :

A hydrogen atom makes a transition from n = 2 to n = 1 and emits a photon. This photon strikes a doubly ionized lithium atom (z = 3) in excited state and completely removes the orbiting electron. The least quantum number for the excited state of the ion for the process is :

Half-lives of two radioactive elements $$A$$ and $$B$$ are $$20$$ minutes and $$40$$ minutes, respectively. Initially, the samples have equal number of nuclei. After $$80$$ minutes, the ratio of decayed number of $$A$$ and $$B$$ nuclei will be: