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Question: Mass of an atom of sodium is \(3.81932\times {{10}^{-23}}\) g. Calculate the atomic mass of sodium i...

Mass of an atom of sodium is 3.81932×10−233.81932\times {{10}^{-23}} g. Calculate the atomic mass of sodium in u (Da).

Explanation

Solution

The unit Dalton which have the unit symbol Da is also a non-SI unit of mass defined as 1 Da = 1 u and One Dalton is equal to 1.6605×10−241.6605\times {{10}^{-24}} grams. Hence in order to convert 3.81932×10−233.81932\times {{10}^{-23}} g into Dalton we need to divide it with 1.6605×10−241.6605\times {{10}^{-24}} g.

Complete step by step answer:
- As we know, the unified atomic mass unit which has the unit symbol u is a non-SI unit of mass, which can be defined as one-twelfth the mass of a single 12C atom in its ground state. This description was approved by both the International Union of Pure and Applied Chemistry (IUPAC) and the International Union of Pure and Applied Physics (IUPAP) in the early 1960s to resolve a long-lasting difference between the two scales of the atomic mass unit.
- The word “atomic mass unit” which have the unit symbol amu also has been used as a unit of mass which is defined as one-sixteenth the isotope-average atomic mass (equivalent to the atomic weight) of oxygen in chemistry and as one-sixteenth the mass of a single atom of oxygen in physics.
- The unit Dalton which have the unit symbol Da is also a non-SI unit of mass defined as 1 Da=1 u and is also accepted as a unit for use by the SI .Hence, both the unified atomic mass unit(u) and Dalton(Da) are approved units for mass of atoms, ions and molecules.
- One Dalton is equal to 1.6605×10−241.6605\times {{10}^{-24}}grams. Hence in order to convert 3.81932×10−233.81932\times {{10}^{-23}} g into Dalton we need to divide it with 1.6605×10−241.6605\times {{10}^{-24}} g.
1Da=1.6605×10−24g1Da=1.6605\times {{10}^{-24}}g
3.81932×10−23g=3.81932×10−231.6605×10−24=23.001Da3.81932\times {{10}^{-23}}g=\dfrac{3.81932\times {{10}^{-23}}}{1.6605\times {{10}^{-24}}}=23.001Da
Therefore, the atomic mass of sodium in u (Da) is 23.001

Note: Keep in mind that, it is a general mistake to use the deprecated unit symbol “amu” and the deprecated term “atomic mass unit” for the unit of mass defined as one-twelfth the mass of single atom 12C^{12}C. Also, the unit symbol “mmu,” which means a milli mass unit, is also a suitable unit in SI and instead of “mmu” 10−3u{{10}^{-3}}u or “mDa” should also be used.