Let A be the mass number, Z be the atomic number and N be the neutron number of a nucleus. Then the statement which is always true, is

Step-by-step solution

The mass number A is the sum of the atomic number Z and the neutron number N , so A = Z + N . Squaring both sides, we get A^2 = (Z + N)^2 = Z^2 + N^2 + 2NZ . Since Z^2 0 and N^2 0 , we have Z^2 + N^2 + 2NZ 2NZ . As N and Z are non-negative integers, 2NZ NZ . Therefore, A^2 NZ is always true. Checking the other options: For A 2N Z + N 2N Z N , which is false for heavy nuclei like ²³⁸₉₂ U where N > Z . For A 2Z Z + N 2Z N Z , which is also false for heavy nuclei. For AN Z^2 (Z+N)N Z^2 ZN + N^2 Z^2 , which is false fo