Question

One atomic mass unit (amu) is approximately equal to ______.
a) $931.4MeV$
b) $251.2MeV$
c) $102.4MeV$
d) $170.5MeV$

Answer 1

Since we know that, 1 amu is defined as $\dfrac{1}{{{12}^{th}}}$ of the mass of an atom of $_{6}{{C}^{12}}$isotope. Also, the mass of an atom of $_{6}{{C}^{12}}$isotope. is $1.99\times {{10}^{-26}}kg$. Now, according to Einstein, the energy is given as:$E=m{{c}^{2}}$. Use this equation to find energy in Joules. Also, we know that, $1J=\dfrac{1}{1.6\times {{10}^{-13}}}MeV$, so find the energy in MeV.

Formula used:
$E=m{{c}^{2}}$, where m is mass and c is speed of light

Complete step by step answer:
Since we know that the mass of an atom of $_{6}{{C}^{12}}$isotope. is $1.99\times {{10}^{-26}}kg$ and 1 amu is equal to $\dfrac{1}{{{12}^{th}}}$ of the mass of an atom of $_{6}{{C}^{12}}$isotope
So, we get:
$\begin{aligned} & 1\text{ }amu=\dfrac{1.99\times {{10}^{-26}}}{12}kg \\\ & =1.66\times {{10}^{-27}}kg \end{aligned}$
Now, we have:
$\begin{aligned} & c=3\times {{10}^{8}}m{{s}^{-1}} \\\ & m=1.66\times {{10}^{-27}}kg \\\ \end{aligned}$
So, by using the formula: $E=m{{c}^{2}}$, we get:
$\begin{aligned} & E=1.66\times {{10}^{-27}}\times {{\left( 3\times {{10}^{8}} \right)}^{2}} \\\ & =1.49\times {{10}^{-10}}J \end{aligned}$
Also, we know that: $1J=\dfrac{1}{1.6\times {{10}^{-13}}}MeV$
So, we get:
$\begin{aligned} & E=\dfrac{1.49\times {{10}^{-10}}}{1.6\times {{10}^{-13}}} \\\ & =931.25MeV \end{aligned}$

Hence, 1 amu is equal to $931.4MeV$.

So, the correct answer is “Option A”.

Note:
Atomic mass units are described as a unit of measurement for atoms and molecules, just like the mass of a person may be expressed in pounds or kilograms. Hydrogen, for example, is the first element on the periodic table and has an atomic number of 1 and an atomic mass of 1.00794 amu, or atomic mass units.