Question

A proton is located at the origin, and then a second proton is located on the x-axis at x = 6.00 fm (1 fm = 10-15 m). (a) calculated the electric potential energy associated with this configuration. (b) an alpha particle (charge = 2e, mass = 6.64 × 10 ―27 kg) is now placed at (x, y) = (3.00, 3.00) fm. calculate the electric potential energy associated with this configuration. (c) starting with the three-particle system, Find the change in electric potential energy if the alpha particle is allowed to escape to infinity while the two protons remain fixed in places. (throughout, neglect any radiation effects.)

Answer 1

The annualized rate of return on the property purchased in 1995 and sold in 2002 can be calculated using the formula for Compound Annual Growth Rate (CAGR):

Step-by-step explanation:

Calculating Electric Potential Energy

To calculate the electric potential energy of a system of charges, we can use the following formula for point charges:

U = k * (q1 * q2) / r

Where U represents the electric potential energy, k is Coulomb's constant (8.99 × 109 Nm2/C2), q1 and q2 are the charges, and r is the distance between the charges. For the part (a), taking two protons each with charge e, the potential energy is:

Upp = k * (e * e) / 6.00 fm

For part (b), where an alpha particle is involved, we must account for its charge being 2e, and calculate its potential energy with respect to each proton, then add those values together to find the total potential energy. The distances from the alpha particle to each proton are determined by using the Pythagorean theorem.

For part (c), as the alpha particle escapes to infinity, its potential energy with respect to the other charges reduces to zero. Therefore, the change in electric potential energy would be the negative of the initial potential energy calculated in part (b).

To find the tunneling probability for an alpha particle, we use the quantum mechanical concept of tunneling, which is usually calculated with a formula derived from the Schrödinger equation.