Force between two particles

[snowborder456]

1. 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*10^-15 m apart, and (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


Equations:

Coulomb's law: (k*(q1)*(q2))/r^2


Attempt:

i did k* (1.6*10^-19)2/ (5*10^-15) for part A and did not get the right answer which is supposed to be 36.8 N

- could someone please tell me how i am supposed to get that answer

- also i am not sure what equation to use for part 2

 

[andrevdh]

You need to square both the distance and double the charge.

 

[Moetasim]

(b)

To calculate the force between two particles, we can use Coulomb's law, which states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. In this case, we have two alpha particles with charges of +2e each, where e is the elementary charge (1.6*10^-19 C). So, the force between them can be calculated as:

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

Where:
k = Coulomb's constant (9*10^9 N*m^2/C^2)
q1, q2 = charges of the particles (+2e each)
r = distance between the particles (5*10^-15 m)

Substituting the values, we get:

F = (9*10^9 * 2*1.6*10^-19 * 2*1.6*10^-19) / (5*10^-15)^2
= 36.8 N

So, the force between the two alpha particles when they are 5*10^-15 m apart is 36.8 N.

For part (b), we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. So, the magnitude of the acceleration of the alpha particles can be calculated as:

a = F/m

Where:
F = force between the particles (36.8 N)
m = mass of the alpha particle (4.0026 u = 6.64*10^-27 kg)

Substituting the values, we get:

a = 36.8 / 6.64*10^-27
= 5.55*10^26 m/s^2

Therefore, the magnitude of the acceleration of the alpha particles due to the force between them is 5.55*10^26 m/s^2.