Question

One atomic mass unit in $amu = 1.66 \times {10^{ - 27}}kg$. The atomic weight of oxygen is 16. The mass of one atom of oxygen is?

(A) $26.56 \times {10^{ - 27}}kg$
(B) $10.53 \times {10^{ - 27}}kg$
(C) $74 \times {10^{ - 27}}kg$
(D) $2.73 \times {10^{ - 27}}kg$

Answer 1

Hint: The atomic weight of oxygen is given in \[amu\]. The conversion factor relating \[amu\] and kg: $1amu = 1.66 \times {10^{ - 27}}kg$. Multiply the atomic weight with the value to get the mass of one atom of oxygen.

Complete step-by-step solution

Atomic mass unit (\[amu\]): In nuclear physics a convenient unit of mass is the unified atomic mass unit abbreviated as \[amu\]. It is sometimes also denoted by u.

Atomic mass unit is defined as one- twelfth (\[ \dfrac{1}{12}th\]) the mass of a carbon – 12 (\[_6{C^{12}}\] ) atom.

It is given that the atomic weight of oxygen\[n{\text{ }} = {\text{ }}16\] \[amu\]. The mass of one atom can be calculated using the given relation,$1amu = 1.66 \times {10^{ - 27}}kg$

Therefore, the mass of one atom of oxygen is

$
  16 \times 1.66 \times {10^{ - 27}} \\

   = 26.56 \times {10^{ - 27}}kg \\

 $
Mass of one atom of oxygen is $26.56 \times {10^{ - 27}}kg$

the correct option is A.

Note: Mass of electron \[ = {\text{ }}9.1{\text{ }} \times {\text{ }}{10^{ - 31}}kg{\text{ }} = {\text{ }}0.0005486{\text{ }}amu\]

Mass of proton \[ = {\text{ }}1.6726{\text{ }} \times {\text{ }}{10^{ - 27}}kg{\text{ }} = {\text{ }}1.007276{\text{ }}amu\]

Mass of neutron \[ = \;1.6750{\text{ }} \times {\text{ }}{10^{ - 27}}kg{\text{ }} = {\text{ }}1.00865{\text{ }}amu\]

Atomic mass unit is also associated with energy in terms of\[\;MeV\], from the Einstein’s mass energy equation \[E{\text{ }} = {\text{ }}m{c^2}\] where\[,{\text{ }}1{\text{ }}amu{\text{ }} = {\text{ }}931{\text{ }}MeV\].