Calculate the level from which the electron fell, n2, for the hydrogen line you observed.
wavelength (lambda) = 400 nm
n1 = 2
RH = 2.18 x 10^-18
I keep having trouble with finding n2. Is the above given right to plug in for 1/(lambda) = RH (1/n1^2 - n2^2)
thank you for any help
no. Your constant is not right.
The Rydberg constant, RH = 1.097E7.
1/wavelenth = RH(1/n1^2 - 1/n2^2)
wavelength must be converted to meters.
Okay, I was solving out this this equation for n2^2
n2^2 = 1(1/n - E/Rh)
Is this right?
If its okay, can you show me in detail how to find n2^2 because I have done this three times and I'm still a little confused by this.
I think it is far easier to substitute the numbers, then do the math than try to manipulate all of the variables. I use one of the following where w = wavelength:
1/w = 2.180E-19/hc x (1/n1^2 - 1/n2^2) but it is much easier to simplify that by
1/w = RH(1/n1^2 - 1/n2^2). That formula is the original Rydberg formula I believe. Using the 2.180 number as well as substituting h and c is just asking for more places for a mistake in my opinion.
ok thank you very much
To calculate the level from which the electron fell, n2, for the hydrogen line you observed, you can use the formula:
1/λ = RH (1/n1^2 - 1/n2^2)
where λ is the wavelength, RH is the Rydberg constant (2.18 x 10^-18), n1 is the initial level (given as 2), and n2 is the level you want to calculate.
In this case, you are given the wavelength (λ) as 400 nm and n1 as 2.
Now, to find n2, you can rearrange the formula as follows:
1/n2^2 = 1/n1^2 - λ/RH
Substituting the given values:
1/n2^2 = 1/(2^2) - (400 nm) / (2.18 x 10^-18)
Simplifying:
1/n2^2 = 1/4 - [(400 x 10^-9) / (2.18 x 10^-18)]
Now, evaluate the right-hand side of the equation:
1/n2^2 = 1/4 - (182,481.75)
Performing the subtraction:
1/n2^2 = -182,481.5
Now, take the reciprocal of both sides of the equation to solve for n2^2:
n2^2 = -1 / (-182,481.5)
Simplifying:
n2^2 = 5.48 x 10^-6
Finally, take the square root of both sides to solve for n2:
n2 = √(5.48 x 10^-6)
n2 ≈ 0.00234
Therefore, the level from which the electron fell, n2, for the hydrogen line observed is approximately 0.00234.