The Rydberg equation, with n1=1, predicts an ultraviolet series of spectral lines of atomic hydrogen. Which of the following wavelengths is not predicted by the equation: 1/ = (1.097 x 10(7) m - 1) x (1/n1(2)-1/n2(2)
Sorry forgot to post the wavelengths.
A) 182nm
B) 103nm
C) 97nm
D) 95nm
E) 91nm
To determine which wavelength is not predicted by the Rydberg equation, we need to plug in different values of n2 into the equation and calculate the corresponding wavelength for each value. Then, we can compare those wavelengths with the given options to find the one that doesn't match.
The Rydberg equation is given by:
1/λ = R_H * (1/n1^2 - 1/n2^2)
where λ is the wavelength, R_H is the Rydberg constant for hydrogen (1.097 × 10^7 m^-1), and n1 and n2 are the principal quantum numbers.
In this case, we are given that n1 = 1, so the equation becomes:
1/λ = R_H * (1/1^2 - 1/n2^2)
Simplifying further:
1/λ = R_H * (1 - 1/n2^2)
Now, let's calculate the wavelengths for different values of n2:
For n2 = 2:
1/λ = (1.097 × 10^7 m^-1) * (1 - 1/2^2)
1/λ = (1.097 × 10^7 m^-1) * (1 - 1/4)
1/λ = (1.097 × 10^7 m^-1) * (3/4)
1/λ ≈ 8.2275 × 10^6 m^-1
λ ≈ 1.21 × 10^-7 m
For n2 = 3:
1/λ = (1.097 × 10^7 m^-1) * (1 - 1/3^2)
1/λ = (1.097 × 10^7 m^-1) * (1 - 1/9)
1/λ = (1.097 × 10^7 m^-1) * (8/9)
1/λ ≈ 9.7511 × 10^6 m^-1
λ ≈ 1.03 × 10^-7 m
For n2 = 4:
1/λ = (1.097 × 10^7 m^-1) * (1 - 1/4^2)
1/λ = (1.097 × 10^7 m^-1) * (1 - 1/16)
1/λ = (1.097 × 10^7 m^-1) * (15/16)
1/λ ≈ 1.0317 × 10^7 m^-1
λ ≈ 9.69 × 10^-8 m
Now, let's compare these wavelengths with the given options to find the one that doesn't match.