Question

One a.m.u is equal to $1.66\times {{10}^{-(20+x)}}$ kg. Find the value of x.

Answer 1

Hint: One a.m.u is $\dfrac{1}{12}$ of the mass of one carbon-12 atom and it is related to the avogadro number. It is the average of the proton rest mass and the neutron rest mass. It is also roughly calculated as the sum of protons and neutrons inside the nucleus.

Formula used:
$a.m.u=\dfrac{1}{{{N}_{a}}}$

Complete answer:
One a.m.u is equal to $\dfrac{1}{12}$ times the mass of a carbon-12 atom and is used to find out masses of atomic and subatomic particles.. It is an arbitrary unit used to measure the particles in the atomic and subatomic levels. The mass of the hydrogen atom is one a.m.u. But we can also say that the molar mass of hydrogen is equal to one gram per mole as both the results are close.
The value of one a.m.u in terms of kilograms is,

$\begin{align}
  & a.m.u=\dfrac{1}{{{N}_{a}}} \\
 & a.m.u=\dfrac{1}{6.022\times {{10}^{23}}} \\
 & a.m.u=1.66\times {{10}^{-24}}g \\
 & a.m.u=1.66\times {{10}^{-27}}kg \\
\end{align}$
On comparing it with the question,

$\begin{align}
  & -27=-(20+x) \\
 & x=7 \\
\end{align}$
Therefore, the value of x is $7$.

Additional Information:
An atomic mass unit (symbolized AMU or amu) is defined as precisely 1/12 the mass of an atom of carbon-12. The carbon-12 (C-12) atom has six protons and six neutrons in its nucleus.
In general terms, one AMU is the average of the proton rest mass and the neutron rest mass. This is approximately 1.67377 $\times$ 10$^{-27}$ kilogram (kg), or 1.67377 $\times$ 10$^{-24}$ gram (g). The mass of an atom in AMU is roughly equal to the sum of the number of protons and neutrons in the nucleus.
The AMU is used to find out the relative masses of various isotopes of elements. Thus, for example, uranium-235 (U-235) has an AMU of approximately 235, while uranium-238 (U-238) is having slightly more mass than uranium-235. John Dalton is the scientist after whom, this unit is named in the 18th century. He is a profound teacher and naturalist. In 2009, Dalton was used as an alternative to a.m.u by an international organisation for standardization in 2009.

Note:
While solving the value of one a.m.u through Avogadro number, the value that we get will be in grams only. So, you have to again convert it into kilograms and then find out the value. Take care about the signs and units.