Questions and Answers of Nuclear Physics

(i) Consider the following data for an RBMK Reactor-Power \(1000 \mathrm{MW}(\mathrm{e}) / 3200 \mathrm{MW}\) th, coolant outlet temperature \(285^{\circ} \mathrm{C}\), Calculate coolant inlet
For the D-D reaction in Eq. (3.1), calculate the amount of energy produced from 1 mole of Deuterium gas and compare it with that of U-235.Data From Equation 3.1:- D+D=He (0.82 eV) + n(2.45 MeV) (3.1)
Explain the difference between isotropic total cross-section and the transport crosssection as in Eq. (5.49). Why transport cross-section is not used in the transport theory?Data From Equation 5.49:-
By using six factor formula for \(k\), derive the Eqs. (7.93), (7.94) of Section 7.7.1. dkoo dp= k MB dM dB 8 + (7.93) 1+M B M B2
Calculate(a) Binding energy per nucleon for \({ }^{235} \mathrm{U}\) and \({ }^{236} \mathrm{U}\).(b) The last neutron-binding energy in \({ }^{236} \mathrm{U}\).\(\Delta=M-A\) is the "mass excess,"
Calculate the energy of the \(\alpha\) particle emitted by \({ }^{235} \mathrm{U}\).\(\Delta=M-A\) is the "mass excess," where \(M\) is the mass of a nuclide and \(A\) its mass number. These data are
The half-life of \({ }^{239} \mathrm{Pu}\) is 24,110 years. Find its mean-life.\(\Delta=M-A\) is the "mass excess," where \(M\) is the mass of a nuclide and \(A\) its mass number. These data are
Find the \(Q\)-value of the reaction: \(\mathrm{Na}^{23}+\mathrm{n}^{1} ightarrow \mathrm{Na}^{24}+\gamma\). Assume kinetic energy of the incident neutron to be negligible.\(\Delta=M-A\) is the "mass
If the initial energy of the neutron is \(2 \mathrm{MeV}\), find the maximum energy loss to the elastically scattered neutron in \({ }^{2} \mathrm{H},{ }^{56} \mathrm{Fe}\), and \({
Density of natural boron is \(2.4 \mathrm{~g} / \mathrm{cc}\). Given: \(\sigma_{a}\) of \({ }^{10} \mathrm{~B}=4000 \mathrm{~b}\), and \(\sigma_{a}\) of \({ }^{11} \mathrm{~B}=0 \mathrm{~b}\). If the
Find the ratio of a narrow SLBW resonance cross-section at a neutron energy \(E=E_{0}+n \Gamma\), to that at the peak, \(n\) being an integer. Calculate the ratio when \(n=2\). \(E_{0}\) is the
If the average logarithmic energy decrement of a material is 0.2 , calculate the number of elastic collisions needed to reduce the neutron energy from \(10 \mathrm{MeV}\) to \(10
The inelastic scattering threshold energies for the first two levels in \({ }^{232} \mathrm{Th}\) are 50 and \(160 \mathrm{keV}\), respectively. Calculate the reaction \(Q\)-values for these
Calculate the kkk-eff of natural uranium sphere of infinite radius, and density 19 g/cc19 g/cc19 g/cc.
Consider a neutron transmission experiment through a \({ }^{232} \mathrm{Th}\) foil of thickness \(0.001 \mathrm{~cm}\). The neutron beam is mono-energetic with a certain energy. Density of the
Find the potential elastic scattering cross-section of neutron for \({ }^{23} \mathrm{Na}\), given scattering radius \(=5.4 \mathrm{fm}\). If the radius were to be obtained as \(1.2 A^{1 / 3}\), what
Assuming a reasonable pattern of cross-section variation, find the capture cross-section of a nuclide at \(0.1 \mathrm{eV}\), if it is 20 barns at \(0.01 \mathrm{eV}\).
The ratio of the natural width to the Doppler width of neutron capture cross-section of a nuclide is 0.1 , for a particular temperature, find the ratio of the resonance peak at that temperature to
The flux in a reactor core shows little variation over a region of energy from 0.4 to \(20 \mathrm{eV}\). Find the average cross-section in this range, if the point cross-sections, given below, show
Calculate the amount of coal required to produce the same energy as that \(1 \mathrm{~kg}\) of U-235. (Assume coal contains 100\% carbon and that combustion of 1 atom of carbon gives \(4
PWR and PHWR use Uranium oxide fuel. Compute and compare the average linear heat rating (LHR) \(\mathrm{W} / \mathrm{m}\) and heat flux at clad surface \(\mathrm{W} / \mathrm{cm}^{2}\) of the two
Calculate the ratio of volume of moderator to the volume of fuel for typical PHWR and PWR lattices using the data given below. Assume that height of the fuel is \(1 \mathrm{~mm}\). It may be noted
Calculate the thermal flux and reaction rate for a PWR core loaded with \(3.4 \mathrm{Te}\) of U-235 and producing \(3200 \mathrm{MW}\) th. Assume that the fission cross section of U-235 for thermal
Fuel utilization is defined as amount of initial fissile material required per unit energy (g/MWd). For example, CANDU uses natural uranium with \(0.71 \%\) U-235 and generates 7.0 GWd/t. It implies
Calculate the number of electrons produced in a \(20 \mathrm{MeV}, 4 \mathrm{~kW}\) LINAC. Also calculate the number for neutrons produced in a \(5 \mathrm{mg}\) Tantallum target for the electron
Calculate the energy gain in ADSS with a \(k=0.98\) and proton energy of \(1 \mathrm{GeV}\) incident on a uranium fuel producing \(200 \mathrm{MeV}\) per fission. Assume that 30 neutrons are produced
Consider four bunches of mono-energetic neutrons with speed \(2000 \mathrm{~m} / \mathrm{s}\) crossing a target as shown in the figure given below. Calculate the total neutron flux in the target
The scattering and absorption cross-sections of \({ }^{12} \mathrm{C}\) for thermal neutrons are \(5.56 b\) and \(0.0035 b\), respectively. Calculate the transport mean free path of neutrons if the
A \(5 \mathrm{~cm}\) thick layer of pure absorbing material with atom density of \(4.0 \times 10^{22}\) nuclei \(/ \mathrm{cm}^{3}\) absorbs \(99.9 \%\) of the incident beam of neutrons. What is the
Two point sources of strength \(S_{0} \mathrm{n} / \mathrm{s}\) are placed in a medium as shown in the figure given below. Derive the expression for the neutron flux and current at point \(P\). So a
Consider an infinitely wide planar isotropic neutron source (in \(\mathrm{Y}-\mathrm{Z}\) plane) located at \(x=0\) and emitting neutrons at the rate of \(S_{0} \mathrm{n} /
Consider a point source of strength \(S_{0}\) located at the center of a sphere (radius R). Assume the medium of sphere is non-multiplying and homogeneous.a. Find the flux distribution in the
Consider an infinite planar neutron source of strength \(100 \mathrm{n} / \mathrm{cm}^{2} / \mathrm{s}\), emitting neutrons in an infinite medium with \(\Sigma_{a}\) and \(D\) as \(2.56
Consider an infinite slab of thickness \(2 A\) placed at the central zone of an infinite moderator. Consider the source within the slab as:Plot the resulting flux distribution from \(-4 A\) to \(4
Derive the expression of neutron flux for a finite bare spherical reactor of radius \(R\). Also find out reactor power \(P\) and the peaking factor. Assume the radius of the spherical reactor is \(50
The geometric buckling of a bare cylinder of radius \(R\) and height \(H\) is given by \(B_{\mathrm{g}}^{2}=\) \((2.4 / R)^{2}+(\pi / H)^{2}\) using one group approximations. Show that the minimum
If \(E^{\prime}\) is the energy of elastically scattered neutron having incident energy \(E\) with a target nuclei of mass \(A\) in the LAB system, show that:where \(\mu\) is the cosine of scattering
Derive the expression for slowing down flux and slowing down density for an infinite homogeneous medium of purely hydrogenous medium with a source of strength \(S\). give a sketch of slowing down
Using nuclear density, demonstrate that neutron-neutron interaction can be ignored while formulating the neutron transport equation.
If \(j(r, E, \hat{\Omega}, t)\) is the angular current density, derive the leakage term for a bound surface. Use Gauss divergence theorem to derive the leakage term (5.11) for a volume domain. r 2. [
If the neutron scattering is isotropic, that is, it does not depend on the scattering angle between incident and outward direction, derive the scattering term given in (5.15) E, [[JdE' [d'vs(E' E Q'
Derive Eq. (5.26) for monoenergetic neutrons, that is, if the cross-sections and the flux do not depend on the incident neutron energies. It may be assumed that the scattering is isotropic. [Q +
Explain basic properties of Legendre's polynomials.
Write Eq. (5.53) for \(l=0\). 8 (x, t) - +(x)y(x,H)= = 1=0 (21+1) 4 ) { (x)P, () [] duw (x, ) P (u') + Q(x, ), (5.53) -1
Derive Eq. (5.60). L 1 n. Vn(1) +(r)n(r) = (21+1)st (r)Y (Qn)d (r) + Q(r, Qn) 1=0 m=0 (5.60)
Prove that the use of the diamond differencing relation (Eq. 5.63) increases the accuracy of the difference approximation. 2Wi Wi+h+Wi-'/ (5.63)
Derive Eqns. (5.65) and (5.67) used for the sweeping procedure. = Vi,n 1+ Zihi 2n -1 hiqi,n Wi-'h,n+2\m\/ (5.65)
Starting from the discretized neutron transport equation, derive corrective equation (5.84) used in the TSA. 8 8-8 8-8 [(1+)3+1+1] = 8-8 8-8 [(4-1)*3+ (--)3] = s (08-08) 18+ 83 = 1 + 1 3 + 1 + 1 f Ag
Using the Chebyshev inequality, prove Eq. (5.210). p(|| ) 0, as N o (5.210)
Use Eq. (5.219) to obtain a large set of random numbers with very large period of repeatability. = Rk (aRk-1+b) mod M,k=1,2,3,... (5.219)
For a one-dimensional domain \((0,1)\), use random number to decide point of neutron generation, use another random number to know its direction of travel, and a third random number to know the point
a) Write the expression for optical distance used in the derivation of Eq. (5.118).b) Eq. (5.118) has been derived for the condition that region \(\mathrm{i}\mathrm{j}\) ? How will the expression of
Can the anisotropic scattering be used in interface current method?
Derive the conservations relations in Eq. (5.144). Nv Ny Ns Pji + Poi=1 P+ ja a=1 Ns B=1 (5.144a) = (5.144b)
Prove that the expansion functions in (5.145) satisfy the orthonormality condition (5.134). 1 W = 2 sind sin w ,a 23 a=32 sind cos@-- , (5.145a) (5.145b) (5.145c)
Derive Eqs. (5.148) and (5.149). 2 Ymax 1 Pji 2 V do - - [ dqp | [Ki (tij) Ki (tij + ti) Ki(t;j+t;) + Ki (tij +t; +t;)] dy, (5.148) 0 Ymin
Derive the collision probability expressions for a lattice cell if an air gap is present after or at the center of fuel region.
Along with Eq. (5.145), take the following functions for orthonormal double P2 expansion of angular flux at the surfaces of lattice cell and derive the expressions fora) components of escape
Solve Eq. (5.178) for one-dimensional annular geometry and calculate the expression for scalar flux. w(s, E)=Wine - ()s 9 + () (1-e-r (E)s), (5.178)
Derive the MOC equation for cluster geometry. How it is different from the MOC equations described for square or hexagonal lattice geometry?
Derive the expressions for modified azimuthal angle and track separation for a hexagonal lattice cell for cyclic tracking.
Calculate the amount of \({ }^{235} \mathrm{U}\) consumed in a year in the Example 6.1. Calculate the burnup in MWd/ \(\mathrm{kg}\) if the reload is 25 tonnes. Also calculate the depletion in \({
(a) Calculate the amount of fissions required in \({ }^{235} \mathrm{U}\) to produce \(1 \mathrm{~W}\).(b) Calculate the fissions required in individual fissile species to produce an assembly power
Calculate the decay power ratio at \(1 \mathrm{~s}, 10 \mathrm{~s}, 10 \mathrm{~min}, 7\) days, and 30 days after shut down for a reactor fueled with \({ }^{235} \mathrm{U}\) operating for 100 days.
Calculate the average linear heat generation rate (LHGR) in a pin for(a) a typical \(6 \times 6\) fuel assembly of a BWR core having 284 fuel assemblies having an active fuel length of \(3.6
(a) Calculate the cycle burnup and in-core average burnup in a BWR using four-batch and six-batch refueling scheme for a discharge burnup of \(40 \mathrm{GWd} / \mathrm{t}\).(b) If the core average
Calculate the fuel burnup in a FBR for a cycle length of 180 days operated at a specific power of \(75 \mathrm{~kW} / \mathrm{kg}\) and compare it with a typical PWR which is operated at \(37
Calculate the RDT for a Pu fueled FBR of \(1200 \mathrm{MWt}\) power operating with \(80 \%\) capacity. The breeding ratio \((B R)\) is 1.1 with \(\mathrm{Pu}\) inventory of approximately 2 tonnes.
What is the average specific power of the fuel in a \(750 \mathrm{MW}\) th PHWR with a residence time to 1 year and the discharge burnup of \(7000 \mathrm{MWd} / \mathrm{t}\). Also calculate this
Calculate the amount of \({ }^{235} \mathrm{U}\) remaining in number of atoms/cc after an irradiation period of 1 year for a \(3 \%\) enriched \(\mathrm{UO}_{2}\) fuel in a thermal reactor with a
Calculate the power produced by \(1 \mathrm{~g}\) of \({ }^{235} \mathrm{U}\) in a thermal reactor operating flux level of \(2.1 \times 10^{14} \mathrm{n} / \mathrm{cm}^{2} / \mathrm{s}\) (Assume
Calculate the residence time required for a fuel with specific power of \(25 \mathrm{~kW} / \mathrm{kg}\) and another of \(150 \mathrm{~kW} / \mathrm{kg}\) to acquire a burnup of 1 atom percent.
Calculate the amount of heat generated in a \(1 \mathrm{~g}\) of \({ }^{238} \mathrm{Pu}\) sample which has half-life of 87.7 years (Consider the alpha energy to be \(5.59 \mathrm{MeV}\) ).
What is the amount of fissile material required to produce \(1 \mathrm{MWd}\) of energy in the following reactors (i) PHWR with a discharge burnup of \(7000 \mathrm{MWd} / \mathrm{t}\), (ii) PWR
Using multiplication factor \(k\) and considering generation wise growth of neutrons,(i) show that \(N(t)=N(0) \exp ((k-1) t / \ell)\).Here \(t\) is the time between first and \(n\)th generation and
Draw graphical representation of Inhour Eq. (7.23). Po=@A+ (w+j) (7.23)
Write point kinetics equations with one group of delayed neutrons and derive the Eqs. (7.42), (7.43) for step change in reactivity, \(ho_{0}\). N(t)=Aet +Aent and C(t) = Boeot + Bent (7.42a) Po-B
Calculate percentage change in mean free path of a neutron in water when water temperature is raised from \(20^{\circ} \mathrm{C}\) to \(300^{\circ} \mathrm{C}\). Water density drop of \(30 \%\) can
For a cylindrical core of a fast reactor, show that in radial expansion of the core, the net reactivity change is negative though the core radial expansion leads to positive re activity addition due
Why does the sodium coolant temperature increase in fast reactors results in negative reactivity coefficient for a small size reactor and positive reactivity coefficient for a large size reactor.
Find out the characteristic dimensions of three square cylindrical reactors; \(A, B\), and \(C\) with core diameter \(=3.5 \mathrm{~m}\). The other needed data of the reactors are given below in
Axial offset control banks are used to maintain desired axial shape in PWRs. They add asymmetric reactivity in axial mode and change the axial offset (tilt). Estimate the approximate change in
Xenon oscillations are a phenomenon at higher levels of power where xenon-135 loss due to neutron capture is dominant. For example, in a typical large thermal environment, if Xe-135 burnup is 10
Explain the plant states considered for safety analysis and the advantages of new states.
Explain the relative criteria that can provide relative safety in nuclear reactors.
What are the functions of regulatory bodies in safety assessment of nuclear reactors?
What are design extension conditions?
Explain fundamental safety principles and the three- and five-levels safety of nuclear reactors.
Explain the difference between DEC-A and DEC-B?
What are the advantages and disadvantages of "Passive Safety" in nuclear reactors?
Explain the deterministic safety assessment (DSA) of nuclear reactors and development growth of this methodology over the years.
What is the probabilistic safety assessment (PSA) and its role in safety assessment of nuclear reactors. Explain the level of maturity achieved by this methodology over the years.
Explain the methodology of evaluating reliability of safety systems.
Explain the uncertainty analysis of DSA, PSA, and Reliability parameters and their advantages.
To achieve a safety goal of ensuring at least \(1 \mathrm{mk}\) of prompt subcriticality following a reactivity excursion event, SCRAM rods are inserted in a few seconds in the core. Find the maximum
Shutdown system terminates the chain reaction in a reactor core immediately following quick insertion of shutoff rods in the core. Reactivity worth of shutoff rods should be adequate enough to
Total fission power in highly thermalized reactor core in equilibrium condition mainly comes from fissions in U-235 and Pu-239. If such a thermal reactor attains a stable reactor period of 1 minute
Explain the important outcomes of the three major accidents occurred in nuclear reactors.
Explain what is a failure mode, failure mechanism, and failure effect in systems.
Show that for two subsystems " \(\mathrm{a}\) " and " \(\mathrm{b}\) " (with reliability \(R_{\mathrm{a}}\) and \(R_{\mathrm{b}}\) ) operating (ex. two pumps supplying fluid flow) in parallel mode

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