The deuteron is bound by nuclear forces just as H-atom is made up of p and e bound by electrostatic forces. If we consider the forces between neutron and proton in deuteron as given in the form of a Coulomb potential but with an effective charge e': `F=1/(4piepsilon_(0)) (e'^(2))/r`
estimate the value of `(e'//e)` given that the following binding energy of a deuteron is 2.2MeV.
The deuteron is bound by nuclear forces just as H-atom is made up of p and e bound by electrostatic forces. If we consider the forces between neutron and proton in deuteron as given in the form of a Coulomb potential but with an effective charge e': `F=1/(4piepsilon_(0)) (e'^(2))/r`
estimate the value of `(e'//e)` given that the following binding energy of a deuteron is 2.2MeV.
estimate the value of `(e'//e)` given that the following binding energy of a deuteron is 2.2MeV.
Text Solution
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The binding energy in ground state of hydrogen atom is `E=(me^(4))/(8 in_(0)^(2)h^(2))=13.6eV.....(i)`
If proton and neutron (in a deutron) had charge e' each, and were governed by the same electrostatic force, then in (i),we replace e and e' and m by m' , the reduced mass of neutron-proton, where
`m'=(MxxM)/(M+M)=M/2=(1836m)/2=918m`
Here, M represented mass of a neutron/proton `:.` Binding energy, `E'=(918me'^(4))/(8 in_(0)h^(2))=2.2MeV.....(ii)`
Dividing (ii) by (i), we get `918((e')/(e^(4)))=(2.2MeV)/(13.6eV)=(2.2xx10^(6))/13.6`
`((e')/(e^(4)))=(2.2xx10^(6))/(13.6xx918)=176.21`
`(e')/(e)=(176.21)^(1//4)=3.64`
If proton and neutron (in a deutron) had charge e' each, and were governed by the same electrostatic force, then in (i),we replace e and e' and m by m' , the reduced mass of neutron-proton, where
`m'=(MxxM)/(M+M)=M/2=(1836m)/2=918m`
Here, M represented mass of a neutron/proton `:.` Binding energy, `E'=(918me'^(4))/(8 in_(0)h^(2))=2.2MeV.....(ii)`
Dividing (ii) by (i), we get `918((e')/(e^(4)))=(2.2MeV)/(13.6eV)=(2.2xx10^(6))/13.6`
`((e')/(e^(4)))=(2.2xx10^(6))/(13.6xx918)=176.21`
`(e')/(e)=(176.21)^(1//4)=3.64`
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