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.
I assume the problem is telling us that the electron travels from N = 6 to n = 2 providing a wavelength of that value.
1/wavelength = R(1/2^2 - 1/6^2)
Solve for R. Wavelength must be in meters.
To calculate the Rydberg constant (RH) using the given λ value and n1 = 2, n2 = 6, you can use the Rydberg equation:
1/λ = RH * (1/n1^2 - 1/n2^2)
Given information:
λ = 0.4118 x 10^(-4) cm
n1 = 2
n2 = 6
Substitute the values into the equation:
1/(0.4118 x 10^(-4) cm) = RH * (1/2^2 - 1/6^2)
Simplify:
1/(0.4118 x 10^(-4) cm) = RH * (1/4 - 1/36)
Next, evaluate the right side of the equation:
1/(0.4118 x 10^(-4) cm) = RH * (9/36 - 1/36)
Combine the fractions on the right side:
1/(0.4118 x 10^(-4) cm) = RH * (8/36)
Simplify further:
1/(0.4118 x 10^(-4) cm) = RH * (2/9)
To isolate RH, divide both sides by (2/9):
(2/9) / (0.4118 x 10^(-4) cm) = RH
Calculate the result on the left side:
RH = (2/9) / (0.4118 x 10^(-4) cm)
Divide the numerator and denominator of the left side separately:
RH = (2/9) / (0.4118) x (10^(-4) cm)
Calculate the value inside the parentheses:
RH ≈ 4.856 x 10^(4) cm^(-1)
The Rydberg equation is given by:
1/λ = RH * (1/n1^2 - 1/n2^2)
We are given the wavelength λ = 0.4118 x 10^(-4) cm, n1 = 2, and n2 = 6. We need to solve for the RH value.
Substituting the given values into the equation, we have:
1/(0.4118 x 10^(-4)) = RH * (1/2^2 - 1/6^2)
Simplifying further:
1/(0.4118 x 10^(-4)) = RH * (1/4 - 1/36)
Now let's evaluate the right-hand side of the equation:
1/(0.4118 x 10^(-4)) = RH * (9/36 - 1/36)
1/(0.4118 x 10^(-4)) = RH * 8/36
Simplifying the right-hand side:
1/(0.4118 x 10^(-4)) = RH * 2/9
Now, let's solve for RH by isolating it on one side of the equation:
RH = (1/(0.4118 x 10^(-4))) / (2/9)
Simplifying further:
RH = (9 / (2 x 0.4118 x 10^(-4)))
Now we can calculate the RH value:
RH = 9 / (2 x 0.4118 x 10^(-4))
Calculating the RH value:
RH ≈ 103413.27 cm^(-1)
Therefore, the RH value is approximately 103413.27 cm^(-1) when n1 = 2 and n2 = 6 in the Rydberg equation.