HW2_solutions - Homework 2 1 Problem The atomic weight A of the only stable isotope of As is 75 There are two stable isotopes of Ga One of atomic weight

Homework 2 1. Problem. The atomic weight A of the only stable isotope of As is 75. There are two stable isotopes of Ga: One of atomic weight 69, occurring with 60.4% abundance. The second isotope has A =71, with natural abundance 39.6%. The atomic mass unit , a.m.u , is the unit which tells us the mass of one unit of atomic weight. Its value is about 1.66 × 10 - 27 Kg. a. Calculate the masses of As and Ga in Kg. For the latter, use as atomic weight the average of the two isotopes weighted by their natural abundances. b. Knowing that GaAs is an fcc crystal like Si, with two atoms per unit cell, knowing also that its lattice constant is 0.565 nm, and using the equation V cell = | a × b · c | , with the fundamental vectors a , b , and c given on page 26 of the Notes, calculate the mass density of GaAs in grams/cm 3 . Solution. The weight of the As ion is m As = 75 × 1 . 66 × 10 - 27 Kg = 1 . 24 × 10 - 25 Kg . The weight of the Ga ion, averaging over the atomic weight of the two isotopes, is m Ga = (69 × 0 . 604 + 71 × 0 . 396) × 1 . 66 × 10 - 27 Kg = 1 . 16 × 10 - 25 Kg .