Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
Atomic mass of `""_56^26"Fe"`, m1 = 55.934939 u
`""_56^26"Fe"` nucleus has 26 protons and (56 − 26) = 30 neutrons
Hence, the mass defect of the nucleus, Δm = 26 × mH + 30 × mn − m1
Where,
Mass of a proton, mH = 1.007825 u
Mass of a neutron, mn = 1.008665 u
∴ Δm = 26 × 1.007825 + 30 × 1.008665 − 55.934939
= 26.20345 + 30.25995 − 55.934939
= 0.528461 u
But 1 u = 931.5 MeV/c2
∴ Δm = 0.528461 × 931.5 MeV/c2
The binding energy of this nucleus is given as:
Eb1 = Δmc2
Where,
c = Speed of light
∴ Eb1 = 0.528461 × 931.5 `(("MeV")/"c"^2) xx "c"^2`
= 492.26 MeV
Average binding energy per nucleon = `492.26/56` = 8.79 MeV
Atomic mass of `""_83^209"Bi"`, m2 = 208.980388 u
`""_83^209"Bi"` nucleus has 83 protons and (209 − 83) 126 neutrons.
Hence, the mass defect of this nucleus is given as:
Δm' = 83 × mH + 126 × mn − m2
Where,
Mass of a proton, mH = 1.007825 u
Mass of a neutron, mn = 1.008665 u
∴ Δm' = 83 × 1.007825 + 126 × 1.008665 − 208.980388
= 83.649475 + 127.091790 − 208.980388
= 1.760877 u
But 1 u = 931.5 MeV/c2
∴ Δm' = 1.760877 × 931.5 MeV/c2
Hence, the binding energy of this nucleus is given as:
Eb2 = Δm'c2
= 1.760877 × 931.5 `(("MeV")/"c"^2) xx "c"^2`
= 1640.26 MeV
Average binding energy per nucleon = `1640.26/209` = 7.848 MeV
संबंधित प्रश्न
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.
What is the significance of binding energy per nucleon of a nucleus of a radioactive element?
Define the terms (i) half-life (T1/2) and (ii) average life (τ). Find out their relationships with the decay constant (λ).
What characteristic property of nuclear force explains the constancy of binding energy per nucleon (BE/A) in the range of mass number ‘A’ lying 30 < A < 170?
Binding energy per nucleon for helium nucleus (2 He) is 7.0 MeV Find value of mass defect for helium nucleus
In a nuclear reactor, what is the function of:
(i) The moderator
(ii) The control rods
(iii) The coolant
Calculate the binding energy of an alpha particle given its mass to be 4.00151 u.
Determine the binding energy per nucleon of the americium isotope \[\ce{_95^244Am}\], given the mass of \[\ce{_95^244Am}\] to be 244.06428 u.
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?
Tritium is an isotope of hydrogen whose nucleus Triton contains 2 neutrons and 1 proton. Free neutrons decay into `p + bare + barν`. If one of the neutrons in Triton decays, it would transform into He3 nucleus. This does not happen. This is because ______.
Explain the release of energy in nuclear fission and fusion on the basis of binding energy per nucleon curve.
State the significance of binding energy per nucleon.
Calculate the values of x and y in the following nuclear reaction.
\[\ce{^227_89Ac -> ^211_82Pb + x[^4_2He]+ y[^0_-1e]}\]
What is binding energy of nucleus?
The binding energy per nucleon of 37Li and 24He nuclei are 5.60 MeV and 7.06 MeV respectively. In the nuclear reaction 3Li7 +1H1 → 2He4 + 2He4 + Q the value of energy Q released is:
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):
Statement I: The binding energy per nucleon, for nuclei with atomic mass number A > 100, decreases with A.
Statement II: The forces are weak for heavier nuclei. In the light of the above statements, choose the most appropriate from the options given below.
Which of the following statements about binding energy per nucleon is incorrect?
