Week13 assignment

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Homework1 PH712

Due at Friday week 14 (31.01.2014, 2pm)

0)

(0 marks): Refresh your knowledge about electronic emissions of photons from ions and atoms.

1a)

(50 marks): Diatomic molecules can radiate energy via rotational transitions.

Show that the energy of a photon by a transition from level J to level J-1 can be determined by:

 

4

2

h

Where J is the rotational quantum number of the upper level, h the Planck constant, r the distance between the two atoms in the molecule (binding length) and µ the reduced mass:

m m

1

m m

2

, where m

1

and m

2

are the individual masses of the atoms in the molecule.

1b)

(50 marks): One of the most common diatomic molecules in the interstellar medium is Carbon Monoxide. This molecule has several stable isotopes (e.g.

12

C

16

O

– CO;

13

CO, C

18

O). All those isotopes can emit light from rotational transitions.

Determine if the spectral resolution required to resolve the transition from CO and

13

CO (for the same J) or from CO and C

18

O is higher (assume that the binding length of all three isotopes is identical).

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