The series in the He+ spectrum that corresponds to the set of transitions where

Question

The series in the He+ spectrum that corresponds to the set of transitions where the electron falls from a higher level into the n = 4 state is called the Pickering series and is an important series in solar astronomy. a) Give an equation that is similar the Rydberg equation for this process. What is the value of the "Rydberg" constant for this system? b) What is the wavelength range for this transition? c) What is the lowest energy transition? d) If a blackbody emitted radiation that had the maximum wavelength as the wavelength emitted in part c, what temperature would it be at? e) Do we consider the Helium atoms to be at that temperature? How are the emission processes different?

Explanation / Answer

As it is the singly ionised He atom, it means, it hydrogenic atom with atomic no., Z=2, and also it is about four times heavier than H-atom.

(a) Rydberg equation - as attached as picture.

Rydberg’s equation in terms of wave number,

And in terms of wavelength -

Where is the Rydberg constant for H-atom taking nucleus mass as infinity as compared to electronic mass, and given by
;

For this problem    

Therefore, Rydberg’s equation is

in terms of Wave number

in terms of wavelength

Rydberg constant for this system is

value of Rydberg constant for this system is 4 times the Rydberg constant.

i.e. R = Z2 *Ri =438948 cm-1

(b) these transition falls in inferared to visible rigion. for example n=5 to n=4 is 10123 angstrom, n=7 to n=4 is 5411 angs etc.

(c) minimum transition energy, this is about 1.23 eV

(d) for temperature T = 14269 K

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