In nuclear fission, a nucleus splits roughly in half.
(a) What is the potential 4.00 10-14 m from a fragment that has 58 protons in it?
(b) What is the potential energy in MeV of a similarly charged fragment at this distance?
To determine the potential at a certain distance from a charged particle, we need to use the formula for electric potential:
V = k*q/r
Where:
V is the electric potential
k is the electrostatic constant (9 x 10^9 N m^2/C^2)
q is the charge of the particle
r is the distance from the particle
Now let's solve the problem step by step:
(a) To find the potential at a distance of 4.00 x 10^-14 m from a fragment with 58 protons, we need to calculate the charge of the fragment first. Each proton has a charge of +1.6 x 10^-19 C.
Charge of the fragment = Number of protons x Charge of one proton
q = 58 * (1.6 x 10^-19 C)
Now we can substitute the value of q into the formula for electric potential:
V = (9 x 10^9 N m^2/C^2) * (58 * (1.6 x 10^-19 C)) / (4.00 x 10^-14 m)
(b) To calculate the potential energy in MeV, we can use the formula:
PE = q * V
Where:
PE is the potential energy
q is the charge of the fragment
V is the electric potential
Substituting the values of q and V that we calculated earlier, we can find the potential energy in MeV. To convert the units, we need to use the equation 1 eV = 1.6 x 10^-19 J.
PE = (58 * (1.6 x 10^-19 C)) * [(9 x 10^9 N m^2/C^2) * (58 * (1.6 x 10^-19 C)) / (4.00 x 10^-14 m)] * (1 eV / 1.6 x 10^-19 J)