Consider that: the tetravalent cation of an isotope has 78 electrons and 128 neutrons; Nuclear relative mass of the same cation is 1.44% higher than the relative nuclear mass of its most common isotope based on these data, calculate the number of neutrons isotope
To calculate the number of neutrons in the isotope, we need to first determine the atomic number of the element for which the isotope belongs. The atomic number corresponds to the number of protons in an atom.
Since the cation has a positive charge of +4, it means that it has lost four electrons from its neutral state. Therefore, the number of protons in the cation would be 78 - 4 = 74.
Next, we calculate the atomic mass of the cation by adding the number of protons and neutrons. In this case, the atomic mass would be 78 (electrons) + 74 (protons) + N (neutrons) = 152 + N.
According to the given information, the nuclear relative mass of the cation is 1.44% higher than the relative nuclear mass of its most common isotope. This implies that the nuclear relative mass of the cation is 1.0144 times the relative nuclear mass of the most common isotope.
To find the relative nuclear mass of the most common isotope, we can subtract 1.44% from 100%: 100% - 1.44% = 98.56%.
Now we can set up an equation to solve for N:
(1.0144)(98.56% of (74 + N)) = 152 + N
Let's solve this equation to find the number of neutrons in the isotope:
1.0144(0.9856(74 + N)) = 152 + N
0.9999(74 + N) = 152 + N
74.0067 + 0.9999N = 152 + N
0.0001N = 152 - 74.0067
0.0001N = 77.9933
N ≈ 779,933 neutrons
Therefore, the number of neutrons in the isotope is approximately 779,933.