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 = 5.
I am not certain of your difficulty here. Can you amplify?
How did you make the symbol for lamda?
(1/lambda) = R(1/n1^2 - 1/n2^2)
Just substitute and solve for R. Use lambda in meters. Post your work if you get stuck. R = 1.0973732 x 10^7 m^-1 if you want to check your answer.
To calculate the RH value using the Rydberg equation, we can start by substituting the given values into the equation:
(1/λ) = R(1/n1^2 - 1/n2^2)
Given:
λ = 0.4118 x 10^-4 cm = 0.4118 x 10^-6 m
n1 = 2
n2 = 5
We need to convert the wavelength from centimeters to meters by dividing by 100:
λ = 0.4118 x 10^-6 m
Now we can substitute the values into the equation:
(1/(0.4118 x 10^-6 m)) = R(1/2^2 - 1/5^2)
Simplifying the equation further:
1/(0.4118 x 10^-6 m) = R(1/4 - 1/25)
1/(0.4118 x 10^-6 m) = R(25/100 - 4/100)
1/(0.4118 x 10^-6 m) = R(21/100)
Now we can solve for R by multiplying both sides by (0.4118 x 10^-6 m):
R = (1/(0.4118 x 10^-6 m)) * (100/21)
R ≈ 1.0973732 x 10^7 m^-1
So the value of RH using n1 = 2 and n2 = 5 is approximately 1.0973732 x 10^7 m^-1.
To calculate the RH value using the given λ value (.4118 x 10^-4 cm) and the Rydberg equation, you need to substitute the values of λ, n1, and n2 into the equation and solve for RH.
The Rydberg equation is as follows:
(1/λ) = R(1/n1^2 - 1/n2^2)
First, convert the given λ value from cm to meters:
λ = .4118 x 10^-4 cm = .4118 x 10^-6 m
Now, substitute the values of λ, n1, and n2 into the equation:
(1/λ) = R(1/n1^2 - 1/n2^2)
(1/.4118 x 10^-6) = R(1/2^2 - 1/5^2)
Simplifying the equation:
2.4288 x 10^6 = R(1/4 - 1/25)
Now, solve for R:
2.4288 x 10^6 = R(25/100 - 4/100)
2.4288 x 10^6 = R(21/100)
To get R alone, divide both sides of the equation by (21/100):
R = (2.4288 x 10^6) / (21/100)
R = 2.4288 x 10^6 * (100/21)
Calculating the RH value:
R = 1.1558 x 10^7 m^-1
So, the RH value using the given λ value (.4118 x 10^-4 cm) and n1 = 2, and n2 = 5 is approximately 1.1558 x 10^7 m^-1.
You can verify your answer by comparing it to the given value of RH, which is 1.0973732 x 10^7 m^-1.