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
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).
In which of the following decays the atomic number decreases?
(a) α-decay
(b) β+-decay
(c) β−-decay
(d) γ-decay
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
In a nuclear reactor, what is the function of:
(i) The moderator
(ii) The control rods
(iii) The coolant
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.
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?
Find the binding energy of a H-atom in the state n = 2
Explain the release of energy in nuclear fission and fusion on the basis of binding energy per nucleon curve.
Calculate the values of x and y in the following nuclear reaction.
\[\ce{^227_89Ac -> ^211_82Pb + x[^4_2He]+ y[^0_-1e]}\]
Find the binding energy per nucleon of 235U based on the information given below.
| Mass(u) | |
| mass of neutral `""_92^235"U"` | 235.0439 |
| mass of a proton | 1.0073 |
| mass of a neutron | 1.0087 |
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):
Binding energy per nucleon is maximum for:
