Calculate the longest wavelength that a line in the Balmer series could have.
See your post below. Both of those sites give you the value and you can calculate them from the formula.
To calculate the longest wavelength in the Balmer series, we need to know the formula that relates the wavelength of a spectral line to the energy levels in an atom.
The Balmer series corresponds to the electron transitions in hydrogen atoms. The formula that relates the wavelength of a spectral line to the energy levels is known as the Balmer formula:
1/λ = R(1/2² - 1/n²)
Where:
λ is the wavelength of the spectral line
R is the Rydberg constant (approximately 1.097 × 10^7 m⁻¹)
n is the principal quantum number of the upper energy level
In the Balmer series, the principal quantum number of the upper energy level is always 2. To find the longest wavelength, we need to find the value of n that gives the largest wavelength. In this case, it would be n = 3.
Substituting the values into the Balmer formula:
1/λ = R(1/2² - 1/3²)
1/λ = R(1/4 - 1/9)
1/λ = R(9 - 4)/36
1/λ = R/36
Rearranging the equation to solve for λ:
λ = 36/R
Now, substituting the value of R:
λ = 36/(1.097 × 10^7 m⁻¹)
Calculating this equation will give us the longest wavelength that a line in the Balmer series could have.