ë 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 have tried to figure this out so many times, found the same answer, and it's always wrong. please help
I thought I showed you how to do this, but as I remember, I used 6 for n2.
I think I know what the problem is.
If we use the known R value of 1.097 x 10^7 and substitute n1 = 1 and n2 = 5, we get
1/wavelength = 1.097E7(1/4-1/25)
1/wavelength = 1.097E7(0.21)
wavelength = 4.34 x 10^-7 meters which is NOT 0.4118 cm (4.118 x 10^-7 m)
In fact, if we substitute 4 for n2 we get 4861 A, n2 = 5 we get 4341 A, n2 = 6, we get 4102 A and n2 = 7 we get 3970 A. None of those are 4118 A (I switched to Angstroms = A and 1 A = 10^-8 cm).
Therefore, I think you can do this calculation till the cows come home and you will not get the accepted value of R. Check your posts. Check your problem. Be sure you are using the right numbers. But I can tell you that 4118 A is not a line of the Balmer Series.
To calculate the Rydberg constant (RH) using the given values n1 = 2, n2 = 5, and the wavelength λ = 0.4118 x 10-4 cm, you can use the Rydberg equation:
1/λ = RH * (1/n1^2 - 1/n2^2)
Rearranging the equation to solve for RH, we have:
RH = (1/λ) / (1/n1^2 - 1/n2^2)
Let's plug the values into the equation:
RH = (1/0.4118 x 10-4 cm) / (1/2^2 - 1/5^2)
First, let's calculate the terms in the denominator:
1/2^2 = 1/4
1/5^2 = 1/25
Now substitute these values back into the equation:
RH = (1/0.4118 x 10-4 cm) / (1/4 - 1/25)
To simplify the expression in the denominator, we need to find a common denominator:
1/4 - 1/25 = 25/100 - 4/100 = 21/100
Now, rewrite the equation:
RH = (1/0.4118 x 10-4 cm) / (21/100)
Next, let's divide the fraction in the numerator:
RH = (100/0.4118 x 10-4 cm) / 21
To simplify, divide the numerator by the denominator:
RH = 100 / (0.4118 x 10-4 cm) / 21
To divide by a fraction, multiply by its reciprocal:
RH = 100 * (21 / (0.4118 x 10-4 cm))
Multiplying the numbers:
RH = (2100 / (0.4118 x 10-4 cm))
Finally, we can simplify the expression:
RH = 5.100 x 10^6 cm-1
So, the RH value, using n1 = 2, n2 = 5, and λ = 0.4118 x 10-4 cm, is 5.100 x 10^6 cm-1.