Question

1 unified atomic mass (1u) is equal to the
$
  {\text{A}}{\text{. 1}}{\text{.66}} \times {\text{1}}{{\text{0}}^{ - 25}}{\text{kg}} \\
  {\text{B}}{\text{. 1}}{\text{.66}} \times {\text{1}}{{\text{0}}^{ - 27}}{\text{kg}} \\
  {\text{C}}{\text{. 1}}{\text{.66}} \times {\text{1}}{{\text{0}}^{ - 29}}{\text{kg}} \\
  {\text{D}}{\text{. 1}}{\text{.66}} \times {\text{1}}{{\text{0}}^{ - 31}}{\text{kg}} \\
 $

Answer 1

Hint: In this question first we need to know the standard definition of Unified Atomic Mass(u) in terms of carbon-12 atoms in ground state. And finding the relationship between the Unified Atomic Mass(u) and the macroscopic SI base unit of mass, the kilogram(kg) to get the value of 1u.
Formula used: Unified Atomic Mass =$\dfrac{1}{{{\text{Avogadro's Number(}}{{\text{N}}_A})}}$

Complete Step-by-Step solution:
Unified Atomic Mass(u): It is a unit of atomic and molecular mass. It is one twelfth of the mass of an unbound carbon-12 atom, at rest and in the ground state.
The relationship of the unified atomic mass unit to the macroscopic SI base unit of mass , the kilogram(kg) is given by Avogadro’s Number(${N_A}$). By the definition of Avogadro’s number, the mass of ${N_A}$ carbon-12 atoms, at rest and in their ground state, is 12 gram.
The value of Avogadro’s number is $6.02214179 \times {10^{23}}$. The Unified Atomic mass(u) is given by $ \Rightarrow 1{\text{u = }}\dfrac{1}{{{N_A}}}$
On putting value of ${N_A}$= $6.02214179 \times {10^{23}}$in above equation we get
 $
   \Rightarrow 1{\text{u = }}\dfrac{1}{{6.22 \times {{10}^{23}}}} \\
   \Rightarrow 1{\text{u = }}1.66 \times {10^{ - 24}}{\text{gm}} \\
 $
Since, above 1u is in grams we have to convert it into kilograms.
We know,
1 kg= 1000gm
$ \Rightarrow 1{\text{u = }}1.66 \times {10^{ - 27}}{\text{kg}}$
Then,
Therefore, 1 unified atomic mass (1u) is equal to the $1.66 \times {10^{ - 27}}{\text{kg}}$.
Hence, option B. is correct.

Note: Whenever you get this type of question the key concept to answer these questions is to learn the definition of terms involved in the question and the conversion of SI units to some other unit like 1 kilogram is equal to the 1000 grams.