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Brackett series of lines are producted w...

Brackett series of lines are producted when electrons excited t high energy level make transitions to the `n = 4` level.
a Determine the longest wavelength in this series.
b Determine the wavelength that corresponds to the transition from `n_(f) = 6 to n_(i) = 4`.

Text Solution

Verified by Experts

a. The longest wavelength corresponds to transition from `n_(f) = 5` to `n_(i) = 4`,the smallest energy change.
So , `(1)/(lambda_(max)) = (1.097 xx 10^(7)) ((1)/(4^(2)) - (1)/(5^(2)))`
`= 2.468 xx 10^(5) m^(-1)`
`lambda_(max) = (1)/(2.468 xx 10^(5)) = 4051 nm`
b. THe wavelength for transition `n_(f) = 6` to `n_(i) = 4` is
`(1)/(lambda) = (1.0947 xx 10^(-7)) ((1)/(4^(2)) - (1)/(6^(2))) = 3.801 xx 10^(5)`
`implies lambda = (1)/(3.801 xx 10^(5)) = 2630 nm`
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