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Brackett Series

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1) Lines in the Brackett series of the hydrogen spectrum are cause by emission of energry accompanying the fall of an electron from outer shells to the fourth shell. The lines can be calculated using the Balmer-Rydberg equation.

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where m = 4, R = 1.097 x 10-2nm-1 , and n is an integer greater than 4. Calculate the wavelengths (in nanometers) and energies (in kilojoules per mole) of the first two lines in the Brackett series. In what region of the electromagnet spectrum do they fall.

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Solution Summary

The solution calculates the energies (in kilojoules per mole) of the first two lines in the Brackett series.

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1/lambda = R (1/m2 - 1/n2 )

R= 0.01097 nm-1
m= 4

1/lambda = 0.00024683 nm-1 =0.01097*((1/4^2)-(1/5^2))
for n= 5
or lambda = 4051 nm

1/lambda = 0.00038090 nm =0.01097*((1/4^2)-(1/6^2))
for n= 6
or lambda = 2625 nm

The wavelengths (in nanometers) and of the first two lines in the Brackett series are
4051 nm and 2625 nm

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