Neutron and Proton densities in a nucleus where N=Z

[sudipmaity]

1. The problem statement, all variables and given/kown data
Assuming that the nuclear radius R=γ₀ *A^(1/3) where γ₀ =1.2×10^(-15) and A is the mass number, Calculate the neutron and Proton densities in a nucleus N=Z.

Homework Equations

A=N+Z.=2Z in this case.
Mass of proton =Z*m_p
Mass of neutron =Z*m_n

The Attempt at a Solution

ρ_n=(m_n*Z)/{4/3 * π *(γ₀ A^(1/3))³}
=3m_n/8π γ₀³
Similarly ρ_p=3m_p/8π γ₀³
Am i right? [/B]

 

[majid313mirzae]

1. The problem statement, all variables and given/kown data
Assuming that the nuclear radius R=γ₀ *A^(1/3) where γ₀ =1.2×10^(-15) and A is the mass number, Calculate the neutron and Proton densities in a nucleus N=Z.

Homework Equations

A=N+Z.=2Z in this case.
Mass of proton =Z*m_p
Mass of neutron =Z*m_n

The Attempt at a Solution

ρ_n=(m_n*Z)/{4/3 * π *(γ₀ A^(1/3))³}
=3m_n/8π γ₀³
Similarly ρ_p=3m_p/8π γ₀³
Am i right? [/B]

yes, you are right. But remember that is only true for a sphere of radius R with charge uniformly distributed throughout its volume