Force between two alpha particles from decaying Be-8 nucleus

[radmonovic]

Ok, the problem is:

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

(a) What is the force between the two alpha particles when they are 3.80e-15 m apart, and

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


Alright, so I used the formula: F = (k q1 q2) / r^2

the radius is given as 3.80e-15, k is 8.99e9, and I am stuck at q1q2

I used 1.6e-19^2 (The charge of a proton, I used it as q1 and q2, so it is squared)

and with that, i got F = 15.94

for part (b), i used F=ma to try to get acceleration. I used the mass of a helium atom and got 3981.90

both were marked incorrect...

i need urgent help, this is the only prob on a webassign I can't get... It is due at 11 tonight, so any help would be greatly appreciated

thanks

 

[radmonovic]

i got the answer

Thanks for all your help guys!

 

[M98Ranger]

for posting this problem and asking for help! Solving problems in nuclear physics can be challenging but also very rewarding. Let's break down the problem step by step to see where you may have gone wrong.

First, let's talk about the force formula you used. The formula you used, F = (k q1 q2) / r^2, is the Coulomb's law equation for electric force. This equation is typically used to calculate the force between two charged particles, such as protons and electrons. However, in this problem, we are dealing with nuclear forces, which are much stronger than electric forces.

The nuclear force between two particles is typically represented by the strong nuclear force constant, which is much larger than the electric constant (k = 8.99e9). Therefore, using the Coulomb's law equation will not give us an accurate result for the force between the alpha particles.

To solve this problem, we need to use the formula for nuclear force, which is F = (k' q1 q2) / r^2, where k' is the strong nuclear force constant (approximately 1.44e23). As for q1 and q2, we cannot simply use the charge of a proton (1.6e-19) squared. The charge of a nucleus is not equal to the charge of a single proton. Instead, we need to use the charge of the entire alpha particle, which is equal to the charge of two protons (2 * 1.6e-19).

So, to calculate the force between the two alpha particles, we have F = (1.44e23 * 2 * 1.6e-19 * 2 * 1.6e-19) / (3.80e-15)^2 = 6.42e-10 N.

Now, for part (b), we can use the force we just calculated and the mass of the alpha particle (4.0015 amu) to solve for acceleration using F = ma. This gives us a = F/m = (6.42e-10 N) / (4.0015 amu * 1.66e-27 kg/amu) = 9.67e17 m/s^2.

I hope this helps you understand where you may have gone wrong and how to correctly solve the problem. Remember, when dealing with nuclear forces, we need to use the appropriate constants and