The emission spectrum of `He^+` ion is the consequence of transition of electron from orbit `n_2` to orbit `n_1` .Given that `2n_2 + 3n_1 = 18` and `2n_2 - 3n_1=6` ,then what will be the total number of photons emitted when the electron transits to orbit `n_1` ?

A) 10

B) 15

C) 21

D) 20

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Transition of the electron from one level (or sublevel) to another is associated with emission of a photon of matching frequency so that,

`DeltaE=(E_2-E_1)=hnu`

For the orbits `n_2` and `n_1` , the given relations are,

`2n_2+3n_1=18`

`2n_2-3n_1=6`

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upon solving, `n_2=6` and `n_1=2`

There are six sublevels in the orbit `n_2` and two sublevels in the orbit `n_1` .

Between them, a total of 6+6=12 transitions are posssible.

So, the given transition must be aasociated with emission of total 12 photons.

Since this is not in the given option, we can think of the possibility of accidental match up of any two pair of transitions, so that the possibilities are reduced by two.

Hence option A) may be the answer.

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