Question

Chromium has four stable isotopes. 4.31% Cr-50, 83.76% Cr-52, 9.55% Cr-53 and 2.38% Cr-54. Calculate the relative atomic mass?
A) 52.1
B) 52.4
C) 51.8
D) None

Answer 1

Hint: For a given element, the relative atomic mass of the element is the weighted arithmetic mean of the masses of all the individual isotopes of the element. We have given abundance of each isotope of chromium. Multiply abundance of each isotope with its atomic mass and then, calculate the average atomic mass of the chromium.

Complete answer:
Isotopes of an element are variants of a particular chemical element which differ in neutron number. All the isotopes of an element have the same number of protons, but different number of neutrons.
Relative atomic mass is nothing but the average weight of the element calculated from all its individual isotopic masses. When the element contains N isotopes, then the expression applied to calculate the average atomic mass ($\overline {{m_a}} $) is as given below:
$\overline {{m_a}} = {m_1}{x_1} + {m_2}{x_2} + ... + {m_N}{x_N}$ .............. (1)
where ${m_1},{m_2},....,{m_N}$ are the atomic masses of each individual isotope and ${x_1}......{x_N}$ are the relative abundances of these individual isotopes.
Here, we are given data of naturally occurring four isotopes of chromium and it is: 4.31% Cr-50, 83.76% Cr-52, 9.55% Cr-53 and 2.38% Cr-54.
Thus, relative atomic mass of chromium will be the average atomic mass calculated from all the individual isotopic mass of each isotope of chromium.
Here, abundance of isotope Cr-50 = 4.31% = 0.0431
Abundance of isotope Cr-52 = 83.76% = 0.08376
Abundance of Cr-53 = 9.55% = 0.0955
Abundance of Cr-54 = 2.38% = 0.0238
Therefore, using the expression (1):
Relative atomic mass of chromium: $50 \times 0.0431 + 52 \times 0.8376 + 53 \times 0.0955 + 54 \times 0.0238 \Rightarrow 52.1g/mol$

Thus, option A is the correct answer.

Note:
Relative atomic mass is mostly used as a synonym for the atomic weight. Relative atomic mass (atomic weight) is also defined as the ratio of average mass of the atom to the unified atomic mass unit (i.e., $\dfrac{1}{{12}}$ of the mass of the C-12 atom).