Which of the following pairs below represents isotopes of the same element?
A. \[{}_{18}^{39}A\] and \[{}_{19}^{39}R\]
B. \[{}_{27}^{60}X\]and \[{}_{28}^{59}Y\]
C. \[{}_{6}^{12}L\]and \[{}_{6}^{14}L\]
D. \[{}_{17}^{37}X\] and \[{}_{17}^{37}X\]
E. \[{}_{2}^{3}E\]and \[{}_{1}^{3}G\]

Hint: Isotopes of the same element that have the same atomic number but different mass numbers. In an element, \[{}_{y}^{x}M\], y denotes the atomic number (number of protons) and x denotes mass number.

Complete step by step answer:
\[{}_{6}^{12}L\]and \[{}_{6}^{14}L\] - Here, the atomic numbers of both the elements are the same, that is, 6. Hence, they represent the same element. Also, their mass numbers are different, that is, 12 and 14. As both the elements have the same atomic numbers and different mass numbers, they qualify as isotopes of the same element.
So, the correct answer is “Option C”.

Additional information:
\[{}_{18}^{39}A\] and \[{}_{19}^{39}R\] - Here, the atomic numbers of A and R are 18 and 19 respectively. This denotes that they represent two different elements. Hence, option A is incorrect.
 \[{}_{27}^{60}X\]and \[{}_{28}^{59}Y\]- Here, the atomic numbers of X and Y are 27 and 28 respectively. This denotes that they represent two different elements. Even though they have different mass numbers, that is 60 and 59, they do not qualify as isotopes of the same element. Hence, option B is incorrect.
\[{}_{17}^{37}X\] and \[{}_{17}^{37}X\] - Here, the atomic numbers of both the elements are the same, that is, 17. Also, their mass numbers are the same, that is, 37. Since they do not have different mass numbers, they do not qualify as isotopes. Hence, option D is incorrect.
\[{}_{2}^{3}E\]and \[{}_{1}^{3}G\] - Here, the atomic numbers of both the elements are different, that is, 2 and 1. This denotes that they do not represent the same element and therefore, they do not qualify as isotopes of the same element. Hence, option D is incorrect.

Note: Since, mass number is a sum of the number of protons and neutrons, isotopes also have different numbers of neutrons apart from having different mass numbers.