Meaning of “average mass” for two atoms
The phrase average mass of two beryllium atoms can refer to the mean mass per atom in a two-atom sample: \(\bar{m} = \dfrac{m_1 + m_2}{2}\). When both atoms are beryllium taken from the same natural sample, the expected mean per atom equals the standard (periodic-table) atomic mass of beryllium.
Numerical values use the common periodic-table average atomic mass of beryllium: \(m_{\mathrm{Be}} \approx 9.0122\,\mathrm{u}\). The atomic mass unit conversion uses \(1\,\mathrm{u} = 1.66053906660\times 10^{-24}\,\mathrm{g}\).
Average mass per atom and total mass for two atoms
\[ \bar{m} = \frac{m_1+m_2}{2}. \]
For two atoms of the same element modeled by the standard atomic mass \(m_{\mathrm{Be}}\), \[ \bar{m} = \frac{m_{\mathrm{Be}}+m_{\mathrm{Be}}}{2} = m_{\mathrm{Be}} \approx 9.0122\,\mathrm{u}. \]
The total mass of the two-atom sample is \[ m_{\text{total}} = m_1+m_2 = 2\,m_{\mathrm{Be}} \approx 2\times 9.0122\,\mathrm{u} = 18.0244\,\mathrm{u}. \]
Conversion to grams
The mass of one atom in grams follows from the atomic mass unit: \[ m_{\mathrm{Be}}(\mathrm{g}) = \left(9.0122\,\mathrm{u}\right)\left(1.66053906660\times 10^{-24}\,\mathrm{g/u}\right) \approx 1.4965\times 10^{-23}\,\mathrm{g}. \]
The mass of two beryllium atoms in grams is \[ m_{\text{total}}(\mathrm{g}) = 2\,m_{\mathrm{Be}}(\mathrm{g}) \approx 2.9930\times 10^{-23}\,\mathrm{g}. \]
Interpretation in a natural-isotope context
The standard atomic mass is a weighted average over naturally occurring isotopes. A two-atom sample can, in principle, contain different isotopes, so \(m_1\) and \(m_2\) can differ. Even in that case, the expected value of the sample mean remains the weighted-average atomic mass: \[ \mathbb{E}[\bar{m}] = \mathbb{E}\!\left[\frac{m_1+m_2}{2}\right] = \frac{\mathbb{E}[m_1]+\mathbb{E}[m_2]}{2} = \mathbb{E}[m] = m_{\mathrm{Be}}. \]
Numerical summary
| Quantity | Expression | Value |
|---|---|---|
| Average mass per atom (two-atom sample) | \(\bar{m} = (m_1+m_2)/2\) | \(\bar{m} \approx 9.0122\,\mathrm{u}\) |
| Total mass of two atoms | \(m_{\text{total}} = 2\,m_{\mathrm{Be}}\) | \(m_{\text{total}} \approx 18.0244\,\mathrm{u}\) |
| Mass of one atom in grams | \(m_{\mathrm{Be}}(\mathrm{g}) = m_{\mathrm{Be}}(\mathrm{u})\times (1\,\mathrm{u})\) | \(\approx 1.4965\times 10^{-23}\,\mathrm{g}\) |
| Mass of two atoms in grams | \(m_{\text{total}}(\mathrm{g}) = 2\,m_{\mathrm{Be}}(\mathrm{g})\) | \(\approx 2.9930\times 10^{-23}\,\mathrm{g}\) |