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## Nuclear Reactions, Physics tutorial

Nuclear Reaction:Nuclear reaction is the procedure whereby mass number or atomic number of target nuclei changes due to bombardment with projectile particles resulting in release of energy. Essential things for nuclear reaction are:

i) Target nucleus

ii) Projectile example

^{1}_{0}n,^{1}_{1}H,^{4}_{2}He,^{ 2}_{1}HX + x → Y + y + Q or X(x,y)Y

e.g.

^{14}_{7}N(α, p)^{17}_{7}O^{14}_{7}N +^{ 4}_{2}He →^{17}_{8}O +^{1}_{1}H + QKinds of Nuclear Reaction

1) F - Fission - X + x → y

_{1}+ y_{2}2) I - Inelastic nuclear reaction - X + x → X

^{k}+x3) T - Transmutation - X + x → Y + y

4) E - Elastic nuclear reaction - X + x → X + x

5) C - Capture - X + x → Y

^{k}Physical qualities that are conserved in any nuclear reaction comprise:

1) Total electric change EZ = K

2) Total number of nuclei EA = K

3) Linear momentum EP = K

4) Sum of mass and energy E(mass + Ke)

5) Parity K

Q - Value Equation:This is nuclear change or amount of energy released in the nuclear reaction. For nuclear reaction, the total rest mass and kinetic energy are conserved.

Example X + x → Y + y + Q

i.e [E

_{X}+ m_{X}C^{2}] + [E_{x}+ m_{x}C^{2}]= [E

_{Y}+ m_{Y}C^{2}] + [E_{y}+ m_{y}C^{2}] + QAs target nucleus X is at rest, then equation turns to

[M

_{x}C^{2}] + [E_{x}+ m_{x}C^{2}] = [E_{y}+ M_{y}C^{2}] + [E_{y}+ M_{y}C^{2}] + QBut Q = change in energy

Hence Q = E

_{x}- (E_{Y}+ E_{y})Q = [(M

_{X}+ m_{x}) - (M_{Y}+ M_{y})]C^{2}Q = Δmc

^{2}Conventional Q-value Equation:Applying principle of conservation of momentum

M

_{x}V_{x}= M_{Y}V_{Y}cosΦ + M_{y}V_{y}cosθ(x-direction)O = M

_{Y}V_{Y}sinΦ + M_{y}V_{y}sinθ(y-direction)Form E = P

^{2}/2m, p^{2}= 2mEThus, momentum mv = √2ME

Equation turns into:

(M

_{x}E_{x})^{1/2 }= (M_{Y}E_{Y})^{1/2}cosΦ + (M_{y}E_{y})^{1/2}cosθO = (M

_{Y}E_{Y})^{1/2}sinΦ + (M_{y}E_{y})^{1/2}sinθSquare equations and add:

M

_{x}E_{x}= M_{y}E_{Y}cos2Φ + M_{y}E_{y}cos2θM

_{x}E_{x}= M_{Y}E_{Y}+ M_{y}E_{y}Minimum energy projectile should have before it can induce nuclear reaction is known as threshold energy

Conservation of linear momentum:M

_{x}V_{x}= M_{c}V_{c}V

_{c }= M_{x}V_{x}/M_{c}But -Q = 1/2M

_{x}V_{x}^{2}- 1/2M_{c}V_{c}^{2}-Q = 1/2M

_{x}V_{x}^{2 }- 1/2M_{c}(M_{x}^{2}V_{x}^{2}/M_{c}^{2})-Q = 1/2M

_{x}V_{x}^{2}[1 - M_{x}/M_{c}]But M

_{c }= M_{X}+ M_{x}-Q = 1/2M

_{x}V_{x}^{2}[1 - M_{x}/(M_{X}+ M_{x})]-Q = 1/2M

_{x}V_{x}2[(M_{X}+ M_{x}- M_{x})/(M_{X}+ M_{x})]-Q = 1/2M

_{x}V_{x}^{2}[M_{X}/(M_{X}+ M_{x})]Take 1/2M

_{x}V_{x}^{2}= E_{thr}-Q = E

_{thr}[M_{X}/(M_{X}+ M_{x})]E

_{thr }= -Q x [M_{X}+ M_{x}/M_{X}]E

_{thr}= -Q x [1 + M_{x}/M_{X}]Nuclear Fission Reaction:This is the reaction that involves splitting of heavy nuclei in two or more lighter nuclei by bombarding heavy nuclei with thermal neutrons and it is generally accompanied with high energy released. Nuclides which can be fissioned by thermal neutrons as follow:

^{235}U,^{237}U and^{239}Pu.Only

^{235}U takes place as expected while others are gotten from fertile materials. Procedure of conversion of fertile materials to fissionable material is referred to as breeder reaction. Energy released in the fission reaction is Q = Δmc^{2}= [(Σm_{i}- Σm_{f})c^{2}]Nuclear Fusion Reaction:This is a combination of two or more light nuclei to form heavier one and this involves supply of high energy. In which this energy will be able to beat coulombs force between them.

^{1}_{1}H +^{2}_{1}H →^{3}_{1}H + γ + QAnd in doing so they should overcome potential barrier that is equal to

V = Z

_{1}Z_{2}e^{2}/4πε_{0}rV = 0.15Z

_{1}Z_{2}Mev, for r = 10^{-14}mThis type of energy (10

^{9}k) can only be attained during nuclear explosions that are not practicable. Generally at this temperature, atoms exist as ions and are collected as plasma. Due to high temperature, it is also referred to as thermonuclear reaction.Tutorsglobe: A way to secure high grade in your curriculum (Online Tutoring)Expand your confidence, grow study skills and improve your grades.

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