Final answer:
The electric force on an electron due to a zirconium nucleus containing 40 protons, with the electron being 1.0 nm away, can be calculated using Coulomb's Law and is found to be 2.9 nN.
Step-by-step explanation:
The calculation of the electric force on an electron by a nucleus can be determined using Coulomb's Law, which states that the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. In the example where the zirconium nucleus contains 40 protons, hence 40 units of the fundamental charge, the force on an electron 1.0 nm away (electric force) can be calculated using the formula F = (k * q1 * q2) / r^2.
To tackle the problem, we need to know that the charge of the nucleus (q1) is 40 times the charge of a proton (which is equal to the fundamental charge e), and the charge of the electron (q2) is equal to -e (the negative indicates it is opposite in sign to the proton's charge). The distance (r) is given as 1.0 nm (1.0 x 10^-9 m). The provided value for k is 8.99 x 10^9 N • m2/C2. Substituting into Coulomb's Law:
F = (8.99 x 10^9 N • m2/C^2 * 40 * 1.602 x 10^-19 C * 1.602 x 10^-19 C) / (1.0 x 10^-9 m)^2
= 2.304 x 10^-9 N, which can be expressed as 2.9 nN, answering the student's question.