NumPy Exercises

NumPy Exercises#

These exercises combine concepts from NumPy Basics and Array Operations.

Work through each exercise, then check your solution.

Exercise 1: Average Atomic Mass#

The isotopes of tin have the following mass numbers and natural abundances:

Mass number	Abundance
112	0.0097
114	0.0066
115	0.0034
116	0.1454
117	0.0768
118	0.2422
119	0.0859
120	0.3258
122	0.0463
124	0.0579

Create two arrays: one for the mass numbers and one for the abundances. Then use vector arithmetic to calculate the average (mean) mass of naturally occurring tin.

Exercise 2: Molecular Distances#

You have an ammonia molecule (NH₃) with the following atomic coordinates (in Ångströms):

atom_N = [0.0, 0.0, 0.0]       # Nitrogen at origin
atom_H1 = [0.0, 0.94, 0.38]    # Hydrogen 1
atom_H2 = [0.81, -0.47, 0.38]  # Hydrogen 2  
atom_H3 = [-0.81, -0.47, 0.38] # Hydrogen 3

In the Loops exercises, you used nested loops to calculate all pairwise distances. Now rewrite this calculation using NumPy arrays to store the atom positions and vector arithmetic to calculate the distances.

Tasks:

Store the atom positions as a 2D NumPy array (4 atoms × 3 coordinates)
Use nested loops to iterate over unique pairs of atoms
For each pair, use NumPy vector arithmetic and np.linalg.norm() to calculate the distance

Exercise 3: Analysis of Experimental Data#

You’ve measurexd the absorbance of a solution at 540 nm over time to monitor a reaction. Here are your measurements (arbitrary units):

times = [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]  # minutes
absorbance = [1.85, 1.52, 1.31, 1.08, 0.89, 0.71, 0.58, 0.49, 0.38, 0.32, 0.28]