Question

there is a brackett series in the hydrogen spectrum where n1=4. Calculate the wavelengths in nm of the first two lines of this series

Answer 1

we know that

for hydrogen series

1/wave length = R [ (1/n1)^2 - (1/n2)^2 ]

for brackett series

n1 = 4

so

1/wave length = R [ 1/16 - (1/n2)^2]

now

n2 starts froom 5

so

for first line

n2 = 5

we get

1/wave length = R [ 1/16 - 1/25]

1/wave length = 0.0225R

so

wave length = 44.444 / R

we know that

R = rydberg constant = 1.097 x 10^7

so

wave length = 44.444 / 1.097 x 10^7

wave length = 4.05 x 10-6 m

wave length = 4050 x 10-9 m

wave length = 4050 nm

2)

for second line

n2 = 6

we get

1/wave length = R [ 1/16 - 1/36]

1/wave length = 0.034722 R

so

wave length = 28.8 / R

we know that

R = rydberg constant = 1.097 x 10^7

so

wave length = 28.8 / 1.097 x 10^7

wave length = 2.625 x 10-6 m

wave length = 2625 x 10-9

wave length = 2625 nm