Question

The mass of an atom of carbon is
(A) 1 g
(B) $1.99\times {{10}^{-23}}g$
(C) $\dfrac{1}{12}g$
(D) $1.99\times {{10}^{23}}g$

Answer 1

Hint: The atomic mass of an element is a weighted average of all the isotopes multiplied by the respective abundance. The carbon atom has two isotopes- Carbon-12 ($^{12}C$) which have 98.93% abundance; and Carbon-13 ($^{13}C$) which have 1.07% abundance.

Complete step by step answer:
-The atomic mass of an element is defined as the average mass of the atoms present in an element and is measured in the atomic mass unit (amu).
-The SI unit of atomic mass is the kilogram, but is often expressed in the non-SI unit called Dalton.
-1 Dalton is defined as $\dfrac{1}{12}$ the mass of a single carbon-12 atom at rest.
-The atomic mass of an atom is constituted majorly by the protons and neutrons present in the nucleus along with the minor contributions of the mass of electrons and nuclear binding energy. Thus, when expressed in Daltons, the numeric value of the atomic mass is nearly the same as the mass number.
$\text{mass constant }{{m}_{u}}=\dfrac{m{{(}^{12}}C)}{12}=1Da$

-We know that 1 mole of C weighs 12 g.
From the mole concept, 1 mole of C contains $=6.022\times {{10}^{23}}$
Therefore, 1 atom of C weighs$=\dfrac{12}{6.022\times {{19}^{23}}}=1.99\times {{10}^{-23}}g$
So, the correct answer is “Option B”.

Note:You should not confuse atomic mass with Standard atomic weight, Mass number, or Relative atomic mass. The weight of an element is the weighted arithmetic mean of all the isotopes; the respective element weighted by each isotope’s abundance on earth is known as the standard atomic weight. The mass number, also called Atomic mass number is the total number of protons and neutrons (nucleons) of an atom. It is approximately equal to the atomic mass of an atom in amu. A dimensionless physical quantity which is the ratio of the average mass of atoms of a chemical element to the atomic mass constant is called Relative atomic mass which is also known as atomic weight.