(a) Emission of microwave radiation from the J = 1→ 0 transition of a molecule has been detected at 88.63 GHz from a region of interstellar space in which there is evidence of thermal equilibrium and a temperature of around 20 K. Estimate the frequency and relative intensity of the J = 2 → 1 transition of the same molecule.

(a) Use the appropriate Uncertainty Principle to calculate the linewidth uncertainty in units of Hz, for an optical emission transition that has a lifetime of τ = 10−9 s. (b) Use calculus to show that an emission transition that has a linewidth of ∆f in frequency, has a linewidth in wavelength given by ∆λ = −(λ^2)/c * ∆f (c) What would be the linewidth in nm, of a transition at 600 nm if it had the lifetime given in part (a)?

Suppose that you have a solution containing a substance whose molecule has two quantum states corresponding to different orientations of a certain subgroup of atoms. The energy difference between these two molecular states is ΔE = 0.10 eV. You are running an experiment where no more than 5% percent of the molecules can be in the higher-energy state, or it will cause unacceptable noise. Can you run the experiment at room temperature, or do you need to cool your solution?

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If density of mercury is 13600 kg/ m = 9.8 m/s?. Find the energy of translation 3 and g %3D per cubic metre of oxygen at N.T.P.

(b) A photon is emitted by a doubly ionised lithium atom (Li²+) when an electron makes a transition to the ground state. The wavelength of the photon is measured to be 10.83 nanometres. Determine the principal quantum number and the energy of the initial state The atomic number of lithium is Z = 3.