Question

If M is atomic mass and A is the mass number, packing fraction is given by:
$A.\dfrac{M}{M-A}$
$B.\dfrac{M-A}{A}$
$C.\dfrac{A}{M-A}$
$D.\dfrac{A-M}{A}$

Answer 1

Hint: The packing fraction value is given by the ratio of the difference between the atomic mass and mass number of an element against the mass number of the element. That is, packing fraction P is P$=\dfrac{M-A}{A}.$

Complete step-by-step answer:
Let’s first understand about the atomic mass ‘M’ and the mass number ‘A’. The atomic mass of an atom is also known as the isotopic mass of the atom. If you closely look at the periodic table, you can see that the atomic masses or the isotopic masses of the elements are not whole numbers. They may be close to a whole number. But, they are not whole numbers.
One the other hand, the mass numbers of the atoms are always whole numbers.
Hence, this difference or variation of isotopic mass and mass number of a specific isotope of an atom is expressed in terms of a quantity known as packing fraction.
The value of packing fraction is equal to the difference of atomic mass and mass number whole divided by the mass number.
That is, packing fraction$=\dfrac{M-A}{A}.$
The value of packing fraction can be both positive and negative alike. A negative value of packing fraction would mean that the mass number is greater than the atomic mass or the isotopic mass.
Similarly, a positive sign of the packing fraction would mean that the value of mass number is greater than the value of atomic mass or isotopic mass.

Note: A negative or positive value of the packing fraction has further meaning to it too. The negative sign of the packing fraction implies that some part of the mass gets converted into energy via Einstein's mass energy relation. This energy is known as the binding energy known normally, and the mass which gets converted into the binding energy is known as mass defect. These kinds of elements are usually very stable.
On the other hand, a positive packing fraction would mean that the atom is somehow less stable. But, this isn’t exactly accurate when considering the elements of low atomic masses.