Question

Why is it impossible for the isotope \({ }_{2}^{2}\) He to exist?

Short answer

The isotope \({ }_{2}^{2}\) He does in fact exist. It is helium with 2 protons and no neutrons.

Step-by-step solution

Understanding isotopes

The isotope notation, \({ }_{Z}^{A}\) X, for an element X is defined as follows: the symbol X identifies the element, while the subscript Z and superscript A represent the atomic number and the atomic mass number of the atom, respectively. The atomic number Z defines the element itself (i.e., the number of protons), while the atomic mass number, A, is the sum of neutrons and protons in the nucleus.

Analyzing the given isotope

When you look at the isotope notation \({ }_{2}^{2}\) He, the superscript 2 refers to the atomic mass number A (sum of neutrons and protons), while the subscript 2, refers to the number of protons in helium (a defining property of helium). However, He is known to have two protons. The 2 protons define an atom as helium.

Conclusion about the impossibility

Considering that the atomic mass number A is 2 (sum of neutrons and protons), and it's known that helium has two protons, this would mean that there are no neutrons in this helium isotope. However, the element still exists as there are two protons which make it helium. Therefore, the isotope \({ }_{2}^{2}\) He does in fact exist, contradicting the premise of the question.