Balmer Wavelength for Hydrogen-like Fe Atom (Z=26): 0.971 nm

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In summary, the conversation discusses a problem involving finding the Balmer wavelength emitted from a hydrogen-like Fe atom with a charge of 26. The correct answer is 0.971 nm, which can be calculated using the equation 1/lambda = R(Z^2)(1/n'^2 - 1/n^2). The conversation also mentions using one of Bohr's equations to solve the problem, but the correct equation for hydrogen-like atoms is 1/lambda = R*Z^2(1/n'^2 - 1/n^2). Thanks to this information from Wikipedia, the correct answer was found.
  • #1
Meekay
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I have been having trouble with this Balmer wavelength problem and was hoping I can get a little guidance.

The question: Find the balmer wavelength (n=3 --> n=2) emitted from a hydrogen-like Fe atom (z=26)

The answer is supposed to be 0.971 nm

My attempt:

1/lambda = R(1/n'^2 - 1/n2)
Since this is a hydrogen-like atom, it should be straight forward

I get lambda = 36/5*R which comes out to be 654 nm

And if I use one of Bohrs equations: E = -Z^2(R/n^2) and E3 = E2+ (hc/lambda) I get a value of 1200 nm
 
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  • #2
I figured it out, my book did not give me this equation for hydrogen-like atoms:

1/lambda = R*Z^2(1/n'^2 - 1/n^2) this gives me 0.97 nm

Thanks wikipedia!
 

1. What is the Balmer Wavelength for Hydrogen-like Fe atom with Z=26?

The Balmer Wavelength for Hydrogen-like Fe atom with Z=26 is 0.971 nm.

2. How is the Balmer Wavelength calculated for Hydrogen-like Fe atom with Z=26?

The Balmer Wavelength is calculated using the Rydberg formula, which is 1/λ = R(Z^2/n^2), where R is the Rydberg constant, Z is the atomic number, and n is the energy level.

3. What is the significance of the Balmer Wavelength for Hydrogen-like Fe atom with Z=26?

The Balmer Wavelength is significant because it is the wavelength of light emitted when an electron transitions from the n=3 energy level to the n=2 energy level in a Hydrogen-like Fe atom with Z=26. This transition is known as the Balmer series and is important for understanding the energy levels of atoms.

4. How does the Balmer Wavelength for Hydrogen-like Fe atom with Z=26 compare to that of Hydrogen?

The Balmer Wavelength for Hydrogen-like Fe atom with Z=26 is longer than that of Hydrogen, which has a Balmer Wavelength of 656.3 nm. This is because the atomic number of Fe is greater than that of Hydrogen, resulting in a stronger electrostatic force and a higher energy transition.

5. Can the Balmer Wavelength for Hydrogen-like Fe atom with Z=26 be experimentally measured?

Yes, the Balmer Wavelength for Hydrogen-like Fe atom with Z=26 can be experimentally measured using spectroscopy techniques. By analyzing the light emitted from a Hydrogen-like Fe atom, scientists can determine the wavelength of the Balmer series and confirm the calculated value.

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