Question

The nucleus of 8Be, which consists of 4 protons and 4 neutrons, isvery 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 are5.00 X 10-15m apart, and (b) what will be the magnitudeof the acceleration of the alpha particles due to this force? Notethat the mass of an alpha particle is 4.0026 u.

Answer 1

36.82304 N

`5.54204* 10^(27)\ m/s^2`

Step-by-step explanation:

k = Coulomb's constant =
`8.99* 10^9\ Nm^2/C^2`

e = Charge of electron =
`1.6* 10^(-19)\ C`

m = Mass of alpha particles =
`4.0026* 1.66* 10^(-27)\ kg`

Charge on alpha particle is given by

`q=2e`

The force is given by

`F=(kq^2)/(r^2)\\\Rightarrow F=(8.99* 10^9* (2* 1.6* 10^(-19))^2)/((5* 10^(-15))^2)\\\Rightarrow F=36.82304\ N`

The force between the two alpha particles are 36.82304 N

Acceleration is given by

`a=(F)/(m)\\\Rightarrow a=(36.82304)/(4.0026* 1.66* 10^(-27))\\\Rightarrow a=5.54204* 10^(27)\ m/s^2`

Magnitude of the acceleration of the alpha particles due to this force is given by
`5.54204* 10^(27)\ m/s^2`