Question

1- For some atom, consider an electron shell corresponding to a principal quantum number n. Answer the questions (a)-(b) below. (a) What is the number of electrons in a fully occupied subshell with a given orbital quantum number l? Explain your answer. (b) What is the number of electrons in a fully occupied shell with a given principal quantum number n? Explain your answer. Hint: For the part (b), use the known mathematical formulas for finite sums: 1 ? ?=0 = ? + 1 , and ? ? ?=0 = ?(?+1) 2 .

2- For an HCP crystal with a given value of the lattice constant a, derive the formula for the smallest possible value of the lattice constant c. Hint: The c value is the smallest when the distance from some atom to its nearest neighbors within the same hexagonally-packed layer equals the distance to its nearest neighbors belonging to a different layer.

Answer 1