# Atomic Mass of Deuterium

1. May 11, 2015

### neilparker62

In the same article which describes the accurate measurement of the Hydrogen 1s-2s transition at:

2 466 061 413 187 035 (10) Hz,

CG Parthey also measures the frequency difference between Hydrogen and Deuterium which he gives as:

670 994 334 606(15) Hz.

Assuming that the transition frequencies for Hydrogen and Deuterium are in the ratio of their reduced masses, I determine the atomic mass of Deuterium according to the following formula.

$\large \frac{m_e\left(1+\frac{\Delta f}{f_h}\right)}{\frac{m_e}{m_p}-\frac{\Delta f}{f_h}}$

The result is 3.3434891661E-27 as compared to the Codata value 3.3435834800E-27

Given the levels of accuracy in Parthey's measurements, there seems to be some discrepancy between the calculated result and the Codata value.

Am I perhaps making an incorrect assumption or am using an incorrect formula ? If not what might be an explanation for this discrepancy ?

2. May 11, 2015

### neilparker62

Sorry - that is to say in the ratio of the electron's reduced mass (Hydrogen) to electron's reduced mass (Deuterium).

3. May 11, 2015

### fzero

I would guess that the discrepancy is because the Dirac energy (2.3) has a nonlinear dependence on $m_e/m_N$. It's hard to quickly determine the order of magnitude of the correction since it ultimately appears in a difference.

4. May 12, 2015

### neilparker62

Could you perhaps try calculating the frequency difference using the Dirac equation with Codata value for atomic mass of Deuterium and then with the above value. See which one predicts better against Parthey's measurement. (I haven't a clue about the Dirac equation so would not be able to do this myself.)

5. May 22, 2015

### theodoros.mihos

Calculations may be on 1s-2p cause 1s-2s can't conserve angular momentum.

6. May 23, 2015

### neilparker62

Perhaps I'm out of depth on theory here but if the 1s-2s transition is 'forbidden' , then how does Parthey measure it ? Same issue arose in another PF discussion on the Lyman Alpha profile.