Demonstrate that the probability of occupying a given vibrational energy level does not depend on whether one includes zero point energy (1/2hcv) or not..

The following are sets of rotational quantum numbers (J,MJ,K). Label each indicated transition as either allowed or forbidden. Hint: Remember the rules for allowed values of the various quantum numbers. a (5,4,0)(3,6,0)b (8,2,2)(9,2,2) c (7,4,2)(7,4,2)d (4,2,5)(3,2,5)

For a particle in a state having the wavefunction =2asinxa in the range x=0toa, what is the probability that the particle exists in the following intervals? a x=0to0.02ab x=0.24ato0.26a c x=0.49ato0.51ad x=0.74ato0.76a e x=0.98ato1.00a Plot the probabilities versus x. What does your plot illustrate about the probability?

Please provide both

The vibrational frequency of 'H2 is 131.9 THz. What is the vibrational frequency of 2H₂ and of ³H₂? Use integer relative masses for this estimate.

d) Write the selection rule for rotational spectrum and define the term used there in. e) Calculate the energy (in ergs) per photon for radiations of A = 400nm. f) Which of the following molecules exhibit rotational spectrum: СО, Н, НВr, Н.0

1. Properties of gasesDetermine the molecular mass M , specific gas constant R, mass-specific energy e fora gas at 500 Kelvin that consists purely of,(a) Carbon dioxide(b) Methane(c) KryptonYou may assume that the vibrational modes are inactive, but explicitly show wherethis assumption enters into your calculations.

2. Given that the vibrational frequency of HCl is 2990.9 cm¹, determine the vibrational frequency (v, in cm¹) of DC1 within the harmonic oscillator approximation.

If the second-lowest energy level of a system is separated from the ground state by 0.5kBT, what will the relative occupations of the first and second energy levels be?

Consider the rotational spectrum of a molecule XY. If the first line in this spectrum is observed at 3.84235 cm, calculate the internuclear distance in nm for the molecule XY. if the masses of X and Y are 19.92168 kg 26.56136 kg and respectively. 0.2761 nm 01356 nm 0.6953 nm 01131 nm