λ for one line of the hydrogen spectrum is .4118 x 10-4 cm. Use this value in the Rydberg equation to calculate the RH value using n1 = 2, and n2 = 6.
To calculate the RH value using the Rydberg equation, you need to know the wavelength (λ) and the values of n1 and n2.
The Rydberg equation is given by:
1/λ = RH * [(1/n2^2) - (1/n1^2)]
Given:
λ = 0.4118 x 10^(-4) cm
n1 = 2
n2 = 6
Substituting these values into the equation, we get:
1/(0.4118 x 10^(-4)) = RH * [(1/6^2) - (1/2^2)]
Simplifying the right-hand side of the equation:
1/(0.4118 x 10^(-4)) = RH * [(1/36) - (1/4)]
1/(0.4118 x 10^(-4)) = RH * [1/36 - 1/4]
Now, let's calculate the right-hand side of the equation:
1/(0.4118 x 10^(-4)) = RH * [(1 - 9/9)/36]
1/(0.4118 x 10^(-4)) = RH * [(8/36)/36]
1/(0.4118 x 10^(-4)) = RH * (8/36) * (1/36)
1/(0.4118 x 10^(-4)) = RH * (8/1296)
Now, isolate the RH term by dividing both sides of the equation by (8/1296):
RH = (1/(0.4118 x 10^(-4))) / (8/1296)
To simplify this, divide the numerator by the denominator:
RH = (1/(0.4118 x 10^(-4))) * (1296/8)
RH = 1296 / (0.4118 x 10^(-4) x 8)
Now, multiply the denominator:
RH = 1296 / (3.2944 x 10^(-4))
Finally, divide 1296 by (3.2944 x 10^(-4)) to get the value of RH:
RH ≈ 3.933 x 10^6 cm^(-1)
Therefore, the value of RH is approximately 3.933 x 10^6 cm^(-1) based on the given values of λ, n1, and n2.