Neutron energy needed to produce fission of 208Pb

[Sswift]

Homework Statement

Estimate the neutron energy needed to produce fission of ²⁰⁸Pb. Is it likely that such neutrons woould be released in the resulting fission?

Homework Equations

E_excitation=Q_excitation+T_n
Q_excitation=[m(²⁰⁸Pb)+m_n-m(²⁰⁹Pb)]c²
V=(e²/4πε_o)(Z₁Z₂/r)
r=1.2fm[(A₁)^1/3+(A₂)^1/3]

The Attempt at a Solution

I'm a little confused just on how to approach this problem. I know that in order to fission the excitation energy must be greater than the activation energy. But doesn't the activation energy depend on what the products of the fission reaction are, of which there is more than one possible combination?

Anyways my best guess was to just come up with a fission reaction that could possibly happen and since Z=50 and N=82 are nuclear shell magic numbers I came up with the following

²⁰⁸Pb + n → ¹³²Sn + ⁷⁵Ge + 2n

using
Q = [m(²⁰⁸Pb)+m_n-m(¹³²Sn) - m(⁷⁵Ge)- 2m_n]

and
E_activation= V - Q

I find the activation energy and then find the kinetic energy the neutron needs for the excitation energy to be greater than the activation energy.

My main problem is I don't know if I'm alright assuming the fission products I did. And as I look around on the internet I get the sense that the activation energy is a set value for a particular isotope, which greatly confuses me. If anyone could just kinda push me in the right direction that would be greatly appreciated!

 

[majid313mirzae]

Homework Statement

Estimate the neutron energy needed to produce fission of ²⁰⁸Pb. Is it likely that such neutrons woould be released in the resulting fission?

Homework Equations

E_excitation=Q_excitation+T_n
Q_excitation=[m(²⁰⁸Pb)+m_n-m(²⁰⁹Pb)]c²
V=(e²/4πε_o)(Z₁Z₂/r)
r=1.2fm[(A₁)^1/3+(A₂)^1/3]

The Attempt at a Solution

I'm a little confused just on how to approach this problem. I know that in order to fission the excitation energy must be greater than the activation energy. But doesn't the activation energy depend on what the products of the fission reaction are, of which there is more than one possible combination?

Anyways my best guess was to just come up with a fission reaction that could possibly happen and since Z=50 and N=82 are nuclear shell magic numbers I came up with the following

²⁰⁸Pb + n → ¹³²Sn + ⁷⁵Ge + 2n

using
Q = [m(²⁰⁸Pb)+m_n-m(¹³²Sn) - m(⁷⁵Ge)- 2m_n]

and
E_activation= V - Q

I find the activation energy and then find the kinetic energy the neutron needs for the excitation energy to be greater than the activation energy.

My main problem is I don't know if I'm alright assuming the fission products I did. And as I look around on the internet I get the sense that the activation energy is a set value for a particular isotope, which greatly confuses me. If anyone could just kinda push me in the right direction that would be greatly appreciated!

It's correct that E_activation= V - Q
if E_activation less than binding energy of last neutron in 209Bi
then a neutron with zero kinetic energy , fission immediately occur
but if E_activation greater than binding energy of last neutron
the difference between them is neutron kinetic energy

 

[majid313mirzae]

also see John .R lamarsh- introduction to nuclear reactor theory chapter 3