Advertisements
Advertisements
प्रश्न
Consider the fission of `""_92^238"U"` by fast neutrons. In one fission event, no neutrons are emitted and the final end products, after the beta decay of the primary fragments, are `""_58^140"Ce"` and `""_44^99"Ru"`. Calculate Q for this fission process. The relevant atomic and particle masses are
`"m"(""_92^238"U")` = 238.05079 u
`"m"(""_58^140"Ce")` = 139.90543 u
`"m"(""_44^99"Ru")` = 98.90594 u
In a fission event of `""_92^238"U"` by fast-moving neutrons, no neutrons are emitted and final products, after the beta decay of the primary fragments, are `""_58^140"Ce"` and `""_44^99"Ru"` Calculate Q for this process. Neglect the masses of electrons/positrons emitted during the intermediate steps.
Given:
`"m"(""_92^238"U")` = 238.05079 u
`"m"(""_58^140"Ce")` = 139.90543 u
`"m"(""_44^99"Ru")` = 98.90594 u
`"m"(""_0^1"n")` = 1.008665 u
Advertisements
उत्तर
In the fission of `""_92^238"U"`, 10 β− particles decay from the parent nucleus. The nuclear reaction can be written as:
\[\ce{^238_92U + ^1_0n -> ^140_58Ce + ^99_44Ru + 10^0_{-1}e}\]
It is given that:
Mass of a nucleus `"m"(""_92^238"U")` m1 = 238.05079 u
Mass of a nucleus `"m"(""_58^140"Ce")`m2 = 139.90543 u
Mass of a nucleus`"m"(""_44^99"Ru")`, m3 = 98.90594 u
Mass of a neutron `"m"(""_0^1"n")`, m4 = 1.008665 u
Q-value of the above equation,
`"Q" = ["m'"(""_92^238"U") + "m"(""_0^1"n") - "m'"(""_28^140"Ce") - "m'"(""_44^99"Ru") - 10"m"_("e")]"c"^2`
Where,
m’ = Represents the corresponding atomic masses of the nuclei
`"m'"(""_92^238"U")` = m1 − 92me
`"m'"(""_58^140"Ce")`= m2 − 58me
`"m'"(""_44^99"Ru")` = m3 − 44me
`"m"(""_0^1"n")`= m4
`"Q" = ["m"_1 - 92"m"_"e" + "m"_4 - "m"_2 + 58"m"_"e" - "m"_3 + 44"m"_"e" - 10"m"_"e"]"c"^2`
`= ["m"_1 + "m"_4 - "m"_2 - "m"_3]"c"^2`
`= [238.05079 + 1.008665 - 139.90543 - 98.90594]"c"^2`
`= [0.248535 "c"^2]"u"`
But 1 u = `931.5 " MeV"//"c"^2`
`"Q" = 0.248535 xx 931.5 = 231.510 "MeV"`
Hence, the Q-value of the fission process is 231.510 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.
Obtain the binding energy (in MeV) of a nitrogen nucleus `(""_7^14"N")`, given `"m"(""_7^14"N")` = 14.00307 u.
What is the significance of binding energy per nucleon of a nucleus of a radioactive element?
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?
In which of the following decays the atomic number decreases?
(a) α-decay
(b) β+-decay
(c) β−-decay
(d) γ-decay
What is the minimum energy which a gamma-ray photon must possess in order to produce electron-positron pair?
Sketch a graph showing the variation of binding energy per nucleon of a nucleus with its mass number.
Answer the following question.
Draw the curve showing the variation of binding energy per nucleon with the mass number of nuclei. Using it explains the fusion of nuclei lying on the ascending part and fission of nuclei lying on the descending part of this curve.
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 ______.
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 ______.
Heavy stable nucle have more neutrons than protons. This is because of the fact that ______.
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.
Nuclei with magic no. of proton Z = 2, 8, 20, 28, 50, 52 and magic no. of neutrons N = 2, 8, 20, 28, 50, 82 and 126 are found to be very stable.
(i) Verify this by calculating the proton separation energy Sp for 120Sn (Z = 50) and 121Sb = (Z = 51).
The proton separation energy for a nuclide is the minimum energy required to separate the least tightly bound proton from a nucleus of that nuclide. It is given by `S_P = (M_(z-1^' N) + M_H - M_(ZN))c^2`.
Given 119In = 118.9058u, 120Sn = 119.902199u, 121Sb = 120.903824u, 1H = 1.0078252u.
(ii) What does the existance of magic number indicate?
Find the binding energy of a H-atom in the state n = 2
State the significance of binding energy per nucleon.
