Advertisements
Advertisements
Question
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 force between neutron and proton in deuteron as given in the form of a Coulomb potential but with an effective charge e′: F = `1/(4πε_0) e^('2)/r` estimate the value of (e’/e) given that the binding energy of a deuteron is 2.2 MeV.
Advertisements
Solution
The binding energy in H atom E = `(me^4)/(8ε_0^2h^2)` = 13.6 eV .....(1)
If proton and neutron had charge e′ each and were governed by the same electrostatic force, then in the above equation we would need to replace electronic mass m by the reduced mass m′ of proton-neutron and the electronic charge e by e′.
`m^' = M/2 = (1836m)/2 = 918m`
∴ Binding energy = `(918me^')/(8ε_0^2h^2)` = 2.2 MeV (given) .....(2)
Diving (2) by (1)
`918(e^'/e)^4 = (2.2 MeV)/(13.6 eV)`
⇒ `e^'/e ≈ 11`.
APPEARS IN
RELATED QUESTIONS
Derive an expression for the total energy of electron in ‘n' th Bohr orbit. Hence show that energy of the electron is inversely proportional to the square of principal quantum number. Also define binding energy.
Write symbolically the nuclear β+ decay process of `""_6^11C` Is the decayed product X an isotope or isobar of (`""_6^11C`)? Given the mass values m (`""_6^11C`) = 11.011434 u and m (X) = 11.009305 u. Estimate the Q-value in this process.
Obtain the binding energy of the nuclei `""_26^56"Fe"` and `""_83^209"Bi"` in units of MeV from the following data:
`"m"(""_26^56"Fe")` = 55.934939 u
`"m"(""_83^209"Bi")`= 208.980388 u
Define the terms (i) half-life (T1/2) and (ii) average life (τ). Find out their relationships with the decay constant (λ).
Is it easier to take out a nucleon (a) from carbon or from iron (b) from iron or from lead?
Which property of nuclear force explains the constancy of binding energy per nucleon `((BE)/A)` for nuclei in the range 20< A < 170 ?
What is the minimum energy which a gamma-ray photon must possess in order to produce electron-positron pair?
Binding energy per nucleon for helium nucleus (2 He) is 7.0 MeV Find value of mass defect for helium nucleus
Calculate mass defect and binding energy per nucleon of `"_10^20 Ne`, given
Mass of `"_10^20 Ne= 19.992397` u
Mass of `"_0^1H = 1.007825` u
Mass of `"_0^1n = 1.008665` u
The figure shows the plot of binding energy (BE) per nucleon as a function of mass number A. The letters A, B, C, D, and E represent the positions of typical nuclei on the curve. Point out, giving reasons, the two processes (in terms of A, B, C, D, and E ), one of which can occur due to nuclear fission and the other due to nuclear fusion.
Calculate the binding energy of an alpha particle given its mass to be 4.00151 u.
The difference in mass of a nucleus and its constituents is called ______.
A body's centre of mass
Mx and My denote the atomic masses of the parent and the daughter nuclei respectively in a radioactive decay. The Q-value for a β– decay is Q1 and that for a β+ decay is Q2. If m e denotes the mass of an electron, then which of the following statements is correct?
Heavy stable nucle have more neutrons than protons. This is because of the fact that ______.
Explain the release of energy in nuclear fission and fusion on the basis of binding energy per nucleon curve.
Which of the following quantities is a measure of stability of nucleus?
Mp denotes the mass of a proton and Mn that of a neutron. A given nucleus, of binding energy B, contains Z protons and N neutrons. The mass M(N, Z) of the nucleus is given by (c is the velocity of light):
Which of the following statements about binding energy per nucleon is incorrect?
Binding energy per nucleon is maximum for:
