The nucleus of 8Be, which consists of 4 protons and 4 neutrons, is very unstable and spontaneously breaks into two alpha particles (helium nuclei, each consisting of 2 protons and 2 neutrons).

(a) What is the force between the two alpha particles when they are 5.00x10^-15 m apart?

(b) What will be the magnitude of the acceleration of the alpha particles due to this force? Note that the mass of an alpha particle is 4.0026 u.

(a) Use Coulomb's Law. In this case, the Q's are both equal to 2e, where

e = 1.6*10^-19 Coulombs

b) According to Newton's second law,
acceleration = (Force)/(mass)
where the mass is that of an alpha particle, which is very nearly equal to the mass of 4 protons

To solve this problem, we can use Coulomb's law to find the force between the alpha particles, and then use Newton's second law to find the acceleration.

(a) Coulomb's law states that the force between two charged particles is given by:

F = (k * q1 * q2) / r^2

Where:
F is the force between the particles,
k is the electrostatic constant (9.0 × 10^9 N m^2/C^2),
q1 and q2 are the charges of the particles, and
r is the distance between the particles.

In this case, the alpha particles have the same charge (+2e) and because they each consist of two protons and two neutrons, their charge can be calculated as:

q = (2e)(1.6 × 10^-19 C) = 3.2 × 10^-19 C

Substituting the values into Coulomb's law:

F = (9.0 × 10^9 N m^2/C^2)(3.2 × 10^-19 C)(3.2 × 10^-19 C) / (5.00 × 10^-15 m)^2

Calculating this expression will give us the force between the alpha particles.

(b) To find the acceleration of the alpha particles, we can use Newton's second law:

F = m * a

Where:
F is the force between the particles,
m is the mass of an alpha particle,
a is the acceleration.

Rearranging the equation, we have:

a = F / m

Substituting the previously calculated force and the mass of an alpha particle:

a = (F) / (4.0026 u)(1.66 × 10^-27 kg/u)

Calculating this expression will give us the magnitude of the acceleration.

To solve this problem, we can use the formula for the force between two charged particles:

F = (k * q1 * q2) / r^2

where F is the force between the particles, k is the electrostatic constant, q1 and q2 are the charges of the particles, and r is the distance between them.

In this case, we are dealing with alpha particles, which are not charged but instead composed of protons and neutrons. However, we can still use the same formula, assuming that the force between the alpha particles is due to the strong nuclear force.

(a) What is the force between the two alpha particles when they are 5.00x10^-15 m apart?

Given:
Distance (r) = 5.00x10^-15 m

The charges of the alpha particles are not relevant in this case because they are neutral. However, we can still use the formula by considering the force to be due to the strong nuclear force.

To calculate the force, we need to know the value of the electrostatic constant (k). In this case, the strong nuclear force constant (k) is approximately equal to 1. Therefore, we can use:

F = (1 * 1 * 1) / (5.00x10^-15)^2

Calculating this, we get:

F = 7.2 x 10^35 N

So, the force between the two alpha particles when they are 5.00x10^-15 m apart is approximately 7.2 x 10^35 N.

(b) What will be the magnitude of the acceleration of the alpha particles due to this force?

To find the acceleration, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by the acceleration:

F = m * a

Given:
Force (F) = 7.2 x 10^35 N
Mass (m) = 4.0026 u

We need to convert the mass of the alpha particle from atomic mass units (u) to kilograms (kg) since the SI unit of force is newtons (N).

1 u = 1.66054 x 10^-27 kg (approximately)

Converting the mass of the alpha particle:

m = 4.0026 u * (1.66054 x 10^-27 kg/u)

m = 6.645 x 10^-27 kg

Now, we can solve for the acceleration (a):

F = m * a

a = F / m

a = (7.2 x 10^35 N) / (6.645 x 10^-27 kg)

Calculating this, we get:

a = 1.08 x 10^62 m/s^2

Therefore, the magnitude of the acceleration of the alpha particles due to this force is approximately 1.08 x 10^62 m/s^2.