Question

3.1) Consider the rotation of the H atom in a HI molecule confined to rotate in a plane (a restriction that will be removed in a subsequent problem). Since the I atom is so much more massive than the H atom, it can be viewed as stationary. The radius of gyration will be taken as the bond length (approximately 160 pm). What wavelengtho radiation is needed to undergo a transition from the ground-state to the first excited state if a) the hydrogen atom is 'H and b) 'H?

Answer 1

In undergo transition from ground state to first excited state (I = emptyset) (I = 0) II = E_I = 1 -E_I = 0 = B times 1 (1 + 1) -B times 0(0 + 1) = 2B = 0 -2B en^-1 where B = constant B = -t/8 pi^2 IC P = plant to to constant I = moment of inertia RHI = 150 Rm = 150 times 10^-12 m mu H I = mH times mI/m_H + m_I mH = absolute mass of H = 1.67343 times 12^-27 kg mI = 125.50447 times 1.57343 times 10^-27 kg/1.008 = 125.8973 times 1.67343 times 10^-27 kg mu HI = 1.67343 times 10^-27 times 125.8973 times 1.67343 times 10^-27 kg^-2/1.67343 times 10^-27 (1 + 125.8473)kg implies 1.66 times 10^-27 kg B = I/8 pi^2 IC = 6.626 times 10^-37 kg m^2 5^-5 times 3/5 times (3.14)^2 times 1.66 times 10^-27 kg times (1.5 times 10^-10)^2m^2 times 3 times 10^8 m5^-1 = 0.0065937 times 10^-34 times 10^27 times 10^20 times 10^-8