(1) Write a program for calculating the wavelengths of emission lines in the spectrum of the hydrogen atom, based on the Rydberg formula. 1 1 m² n2 [2] In nuclear physics, the semi-empirical mass formula is a formula for calculating the approximate nuclear binding energy B of an atomic nucleus with atomic number Z and mass number A: (А - 2Z)2 a5 B = a1A – A2A²/3 – az- A A1/2 ' where, in units of millions of electron volts, the constants are ai = 15.67, az = 17.23, as = 0.75, as = 93.2, and if A is odd, as = 12.0 if A and Z are both even, -12.0 if A is even and Z is odd. a) Write a program that takes as its input the values of A and Z and prints out the binding energy for the corresponding atom. Use your program to find the binding energy of an atom with A = 58 and Z = 28. (Hint: The correct answer is around 490 MeV.) b) Modify your program to print out not the total binding energy B, but the binding energy per nucleon, which is B/A. c) Now modify your program so that it takes as input just a single value of the atomic number Z and then goes through all values of A from A = Z to A = 3Z, to find the one that has the largest binding energy per nucleon. This is the most stable nucleus with the given atomic number. Have your program print out the value of A for this most stable nucleus and the value of the binding energy per nucleon. d) Modify your program again so that, instead of taking Z as input, it runs through all values of Z from 1 to 100 and prints out the most stable value of A for each one. At what value of Z does the maximum binding energy per nucleon occur? (The true answer, in real life, is Z= 28, which is nickel. You should find that the semi-empirical mass formula gets the answer roughly right, but not exactly.)