Question

An element P has two isotopes with relative abundance of 65% and 35%. If the mass number of the two isotopes is X and 31 respectively find the mass number represented by X given that relative atomic mass of element P is 30

Answer 1

Average atomic mass =
65*X + 35*31/100
30 = 65* X + 35*31 /100
3000 - 1085 = 65X
1915=65X
X = 1915/65 = 29.46

Answer 2

Answer:

Explanation:

Concept:

Isotope:

Isotopes are members of the same element's family but have variable numbers of neutrons despite having the same number of protons. The atomic number of an element on the Periodic Table is determined by the number of protons in its nucleus. For instance, the atomic number 6 of carbon has six protons.

Relative abundance:

The proportion of atoms with a particular atomic mass that can be found in a naturally occurring sample of an element is known as the relative abundance of an isotope.

Relative atomic mass:

A dimensionless physical quantity known as relative atomic mass  or atomic weight is defined as the ratio of the average mass of atoms of a chemical element in a particular sample to the atomic mass constant. The definition of the atomic mass constant (symbol: mu) states that it is equal to 1/12 the mass of an atom of carbon-12.   Since the ratio's two components are masses, the final value has no dimensions, which is why it is referred to as relative.

Given:

An element P has two isotopes with relative abundance of 65% and 35%

the mass number of the two isotopes is X and 31.

atomic mass of element P is 30.

Find:

mass number of X.

Solution:

given element P has two isotopes with relative abundance of 65% and 35%

the mass number of the two isotopes is X and 31.

            Average atomic mass =f1m1 + f2m2

Here f represents the fraction of the relative abundance.

Average atomic mass  $= f1m1 + f2m2$

                                     $=\frac{65}{100} *X + 35*\frac{31}{100}$

                                $30 = \frac{65}{100} * X + 35*\frac{31}{100}$

                                $3000 - 1085 = 65X$

                                 $1915=65X$

                                 $X =\frac{1915}{65}$

                                 $X= 29.46$

Hence mass number(X) = 29.46

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