Complete the table below:
The hydrogen emission spectrum has four series (or sets) of lines named Balmer, Brackett, Paschen, and Lyman. Indicate the energy (infrared, ultraviolet, or visible), the nf value for each series, and all possible ni values up to 7. ( Separate the values with commas from lowest to highest. The display will look odd with preceding commas, but that is normal.)
Series Energy nf ni
Balmer VISIBLE
Brackett INFRARED
Paschen INFRARED
Lyman ULTRAVIOLET
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Thank you Dr. Bob!
To complete the table, we need to determine the energy range (infrared, ultraviolet, or visible) for each series, as well as the nf and ni values for each series up to 7.
1. Balmer Series:
The Balmer series lies in the visible spectrum.
To find the nf and ni values for the Balmer series, we can use the following formula:
1/λ = R_H * (1/nf^2 - 1/ni^2)
Where λ represents the wavelength of the emitted light (which determines the energy range), R_H is the Rydberg constant for hydrogen, nf is the final energy level, and ni is the initial energy level.
For the Balmer series, nf = 2 (this is constant for all lines in the Balmer series).
To find the values of ni, we substitute nf = 2 into the equation and solve for ni:
1/λ = R_H * (1/2^2 - 1/ni^2)
1/λ = R_H * (1/4 - 1/ni^2)
1/λ = R_H * (ni^2 - 4) / (4 * ni^2)
λ = (4 * ni^2) / (R_H * (ni^2 - 4))
Now we can substitute λ values corresponding to infrared, ultraviolet, and visible spectra to find the ni values.
2. Brackett Series:
The Brackett series lies in the infrared spectrum.
Using the same formula as above, we can find the nf and ni values for the Brackett series.
nf = 4 (constant for all lines in the Brackett series)
λ = (4 * ni^2) / (R_H * (ni^2 - 16))
3. Paschen Series:
The Paschen series also lies in the infrared spectrum.
Using the same formula as above, we can find the nf and ni values for the Paschen series.
nf = 3 (constant for all lines in the Paschen series)
λ = (4 * ni^2) / (R_H * (ni^2 - 9))
4. Lyman Series:
The Lyman series lies in the ultraviolet spectrum.
Using the same formula as above, we can find the nf and ni values for the Lyman series.
nf = 1 (constant for all lines in the Lyman series)
λ = (4 * ni^2) / (R_H * (ni^2 - 1))
Now, let's complete the table:
Series Energy nf ni
Balmer Visible 2 3, 4, 5, 6, 7
Brackett Infrared 4 5, 6, 7
Paschen Infrared 3 4, 5, 6, 7
Lyman Ultraviolet 1 2, 3, 4, 5, 6, 7