How Does Heavy Hydrogen Affect the Wavelength of the Balmer Series?

In summary, the conversation discusses the difference in wavelength between the first line of the Balmer series in ordinary hydrogen and "heavy" hydrogen. The difference is very small due to the change in the center of mass of the electron-nucleus system. The Bohr model is referenced to understand the impact of electron mass on energy levels, with the reduced mass being used in the calculations. Ultimately, the conversation concludes that the change in wavelength is very small and can be understood through the Bohr model.
  • #1
pi-r8
138
30
Ok, for this one problem, I'm supposed to figure out the difference in wavelength between the first line of the Balmer series in ordinary hydrogen (M= 1.01 u) and in "heavy" hydrogen (M = 2.01 u). The balmer series is when the lowest n is 2, by the way. I already know that the wavelength for the first line of the series in ordinary hydrogen is 656.1 nm, but the answer to this question is supposed to be 0.178 nm, and I can't figure out any way to calculate a wavelength for heavy hydrogen that would give a difference that small. It seems like, no matter what I do, I keep getting half the wavelength of regular hydrogen. Anyone know what to do on this one?
 
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  • #2
The change in wavelength would be very small because a "heavy hydrogen" nucleus has the same charge as a normal hydrogen nucleus, so it exerts roughly the same force on the electron. However, the center of mass of the electron-nucleus system will change. Can you see how this might effect the energy levels (and thus, the wavelengths)?
 
  • #3
Check out the Bohr model and you will see that the electron mass plays a role in the energy level.

But the mass to use is the reduced mass mer=me.mp/(me+mp).
As you can see the change in mer is very small as mp/(me+mp) is nearly 1 as for both cases mp=1.01 or 2.01 as me = 1/1800 mp.

Using the Bohr model you will get a good indication of the magnitude of the deviation
 
  • #4
Thanks guys! I got it.
 

Related to How Does Heavy Hydrogen Affect the Wavelength of the Balmer Series?

1. What is the Balmer series?

The Balmer series is a series of spectral lines in the visible region of the electromagnetic spectrum that are emitted by hydrogen atoms when their electrons transition from higher energy levels to the second energy level.

2. How was the Balmer series discovered?

The Balmer series was discovered by Swiss physicist Johann Balmer in 1885, who noticed a pattern in the wavelengths of visible light emitted by hydrogen atoms. He derived a formula that accurately predicted the wavelengths of the spectral lines.

3. What are the wavelengths of the Balmer series lines?

The wavelengths of the Balmer series lines are 656.3, 486.1, 434.0, 410.2, and 397.0 nanometers. These correspond to the colors red, blue-green, violet, indigo, and purple respectively.

4. What is the significance of the Balmer series?

The Balmer series is significant because it was one of the first major discoveries in the field of quantum mechanics. It provided evidence for the existence of discrete energy levels in atoms and helped to lay the foundation for modern atomic theory.

5. Can the Balmer series be observed in other elements?

Yes, similar series of spectral lines can be observed in other elements besides hydrogen, such as helium, lithium, and sodium. These series are known as the Lyman, Paschen, and Brackett series, respectively, and they correspond to different energy level transitions in each element.

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