Hydrogen exhibits several series of line spectra in different spectral regions. For example the Lyman series (nf = 1 in Balmer-Rydberg equation) occurs in the ultraviolet region while the Balmer (nf = 2) series occurs in the visible range and the Paschen (nf = 3), Brackett (nf = 4) and Pfund ( nf = 5) series all occur in the infrared range. What is the wavelength (in nm) of a line in the Balmer series where ni = 6? Please help!!
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To find the wavelength of a line in the Balmer series where ni = 6, we can use the Balmer-Rydberg equation:
1/λ = R * (1/ni^2 - 1/nf^2)
Where:
- λ is the wavelength of the line (in meters)
- R is the Rydberg constant (approximately 1.097 x 10^7 m^-1)
- ni is the initial energy level
- nf is the final energy level
In this case, ni = 6 and the nf is not specified. We know the Balmer series occurs when nf = 2. Therefore, we can substitute these values into the equation:
1/λ = R * (1/6^2 - 1/2^2)
Simplifying further:
1/λ = R * (1/36 - 1/4)
1/λ = R * (1/36 - 9/36)
1/λ = R * (-8/36)
1/λ = -8R/36
To find the wavelength, we can take the reciprocal of both sides:
λ = 36 / (-8R)
Now we can substitute the value of the Rydberg constant:
λ = 36 / (-8 * 1.097 x 10^7)
Calculating this gives us the wavelength in meters. To convert it to nanometers, we can multiply by 10^9:
λ = 36 / (-8 * 1.097 x 10^7) * 10^9
Simplifying further:
λ ≈ -411.3 nm
The resulting wavelength is negative, indicating that this line in the Balmer series where ni = 6 does not exist in the visible spectrum.