Question

Given,\[_y^xA\] and \[_q^pB\] are isotopes. Which equation is correct regarding the two atoms?
A.\[\left( {{x^2} - {p^2}} \right)\left( {{y^2} - {q^2}} \right) = 0\]
B.\[\left( {{x^2} + {p^2}} \right)\left( {{y^2} + {q^2}} \right) = 0\]
C.\[\left( {{x^2} - {q^2}} \right)\left( {{y^2} - {p^2}} \right) = 0\]
D.\[\left( {{x^2} + {q^2}} \right)\left( {{y^2} + {p^2}} \right) = 0\]

Answer 1

Hint: Isotopes are chemical elements that have different mass numbers but the same atomic numbers. Given isotopes are \[_y^xA\] and \[_q^pB\] , the variables that were written at the bottom were known as atomic numbers and the variables that were written on the top were known as mass numbers.

Complete answer:
A chemical element may have two or more than two isotopes, for example, hydrogen has three isotopes namely proton, deuterium, and tritium.
Given are the two elements namely A, and B. These elements have the atomic numbers \[y\] and \[q\] mass numbers as \[x\] and \[p\] . As given that these were the isotopes, the variables \[y\] and \[q\] will be equal.
The atomic number was represented by \[Z\] in general, given by the number of protons and the mass number was represented by \[A\] which is given by the number of protons and neutrons.
Thus, the term \[{y^2} - {q^2}\] will be equal to zero, as \[y\] and \[q\] are the same numbers nothing but the atomic number which is given by the number of protons. Though this term is multiplied by any other term, the value will be equal to zero only.
Thus, the equation \[\left( {{x^2} - {p^2}} \right)\left( {{y^2} - {q^2}} \right) = 0\] is the true.
Thus, when \[_y^xA\] and \[_q^pB\] are isotopes. The equation \[\left( {{x^2} - {p^2}} \right)\left( {{y^2} - {q^2}} \right) = 0\] is correct regarding the two atoms.

Note:
Isotopes are chemical elements that have the same atomic number but different mass numbers. The atomic number is equal to the number of protons and the mass number is equal to the number of nucleons. Nucleons are the sub atomic particles that were found in the nucleus which are neutrons and protons.