α-Decay:
α-particles are stable and show definite range when they transverse a medium. For α decay to be possible there is minimum energy requirement.
X (A, Z) → Y(A-Y, A-Z)
AXX→A-4Z-2Y + 4zα + Qα
Where Qα = Δmc2
As mass defect between mi and mf (initial and final masses).
mi = [M(A,Z)] = ZMP + NMN - EBi
mf = [M(A-4, Z-2)] = (Z-2)MP + (N-2)MN - EBf
Mα = [M(4,2)] = 2MP + 2MN - EBα
Qα = mi - mf - mα
= -EBi + EBf + EBα
= EBα + EBf - EBi
And EBα = 28.3MeV
Qα = (28.3 + ΔEB)MeV
From semi-empirical formula
Binding energy = E(Z, A)
Thus, disintegration energy of nuclei Qα or total energy released in α-decay is provided as
Qα = 28.3 + (2E/2A)2ΔA + (2E/2Z)AΔZ
α emission is not possible if Qα < O that is Qα should be > 0
It has been found that Qα > O for nuclide for which Z > 82
Assume, mass of parents = MP.
Mass of daughter= Md
Mass of α particle= Mα
Velocity of α particle when emitted = Vα
Velocity of record of daughter = Vd
From conservation of momentum
MαVα = MdVd
Total energy = Qα = final kinetic energy - initial kinetic energy
Qα = 1/2MαVα2 + 1/2MdVd2
Vd = MαVα/Md
By substituting
Qα = 1/2MαVα2 + 1/2Md[MαVα/Md]2
Qα = 1/2MαVα2 + 1/2Mα2Vα2/Md
= 1/2MαVα2[1 + Mα/Md]
For small approximation
Mα/Md ≈ 4/(A-4)
Qα = 1/2MαVα2[1 + 4/(A - 4)]
Qα = Eα[4/A-4 + 1]
= Eα[4+A-4/A-4]
Qα = Eα[A/A-4]
As A is large
Qα ≈ Eα
This signifies most of the energy released is carried away by α-particle.
Range of α -Particle:
α - particles are closely ionizing and lose their energies in rapid succession in air or any medium. Number of ions pairs generated per unit length is known as specific ionization (S.I). Mean distance travelled by α -particle before absorption is known as range.
Intersection of α -particle with atoms or molecules of the medium are entirely statistical and thus they don't have same range as in air.
Range, R = 318E3/2
Empirical relation between range of α-particle and disintegration constant is provided by Geiger Nuttall Law
logλ = AlogR + B
α-decay paradox:
As α-particle is tightly bound entity we can declare it pre-exists in nucleus before its emission. For α-particle to come out or go in nucleus it implies it should have energy in neighborhood of potential well of nucleus.
Energy of α-particle generally ranges between 4-8Mev that is far less than what is needed to overcome potential barrier. Naturally it is not possible to understand this as it has no chance of leaving nucleus.
In 1928, George Gamow considered α -particles as matter wave. This signifies that α-particle as finite probability of penetrating wall of thickness where it suffers series of collisions per second.
β Decay:
Decay procedure in which charge of nucleus changes without change in number of nucleons. There are three kinds of β decay:
i) β- decay: e.g.
AZX→AZ+1Y + 0-1β + v ‾
125B→126C + β + v ‾
ii) β+ decay: e.g.
AZX→AZ-1Y + 0-1β + v ‾
127B→126C + β + v ‾
iii) Electron capture or k-capture: Procedure through which nucleus captures orbital electron, most frequently from closest shell to convert a proton to neutron.
AZX+ 0-1e → AZ-1Y + v ‾
74Be + 0-1e → 73li + v ‾
Energetic of β- decay:
AZX→AZ+1Y + β- + v ‾
In terms of nuclear masses:
Q/C2 = Mn(AZX) - Mn(AZ+1Y)-Me
And in terms of atomic masses:
Q/C2 = Ma(AZX) -Ma(Az+1Y)
For β- to be possible: Q>0
β+ Decay:
AZX→AZ-1Y + β-1 + v ‾
Nuclear masses:
Q/C2 = Mn(AZX) - Mn(Az-1Y)-Me
Atomic masses:
Q/C2 = Ma(AZX) - Ma(Az-1Y) - 2Me
Electron capture:
Q/C2 = Ma(AZX) - Ma(Az-1Y)
β-spectrum:
i) Unlike α-rays, spectrum of β-rays occurs continuous that is electrons emitted have different kinetic energies.
ii) It is also an energy transition between two definite energy states.
iii) Mono-energetic β-rays forming line spectrum are expected.
Most of electrons are emitted with only 1/3 of energy. Thus, this makes one to imagine where remaining of 2/3 of maximum energy would have gone to.
As measurements like momentum and angular momentum are not conserved. These recommend that third particle should exist that always accompany β-decay. It was detected to be neutrino (μ).
Neutrino (μ):
1. Carries away energy equal to energy different between observed energy for β-decay and maximum energy of continuous spectrum.
2. To maintain principle of conservation of energy, neutrino was given following properties
i). 0 charge ii).0 mass iii). Moves with speed of light iv). Spin of 1/2(h/2π)
3. Antiparticle of neutrino, (antineutrino) has given properties
i) 0 charge ii) 0 mass iii) Spin of 1/2(h/2π)
γ - Decay:
When the nucleus is in excited gamma rays are emitted and it is brought to ground state. Nucleus is generally left in excited state after emitting either α or β rays then it is de-excitated by emitting gamma rays. Gamma rays are emitted with discrete and definite energies that is indication of nuclear structure. Energy carried away is ΔE = hf
When mean life time of excited nucleus is >10-6 sec., daughter nucleus is said to show nuclear isomerism.
γk and γ are nuclear isomers and are chemically and physically the same. Difference is that γk is more energetic than γ and it finally emits energy as γ ray and returns to ground state. At times, instead of γ ray being emitted, this excess energy of excited nucleus may be transferred to the extra nuclear electron to get it from shell (generally K or L shell). This procedure is known as internal conversion.
Kinetic energy of converted electron is
Ke = ΔE - Be
Be = binding energy of electron
ΔE = Ei - Ef
Usually, due to internal conversion, yield of γ rays in particular decay <100%. Some spikes observed in continuous β- spectrum is generally because of internal conversion process.
Tutorsglobe: A way to secure high grade in your curriculum (Online Tutoring)
Expand your confidence, grow study skills and improve your grades.
Since 2009, Tutorsglobe has proactively helped millions of students to get better grades in school, college or university and score well in competitive tests with live, one-on-one online tutoring.
Using an advanced developed tutoring system providing little or no wait time, the students are connected on-demand with a tutor at www.tutorsglobe.com. Students work one-on-one, in real-time with a tutor, communicating and studying using a virtual whiteboard technology. Scientific and mathematical notation, symbols, geometric figures, graphing and freehand drawing can be rendered quickly and easily in the advanced whiteboard.
Free to know our price and packages for online physics tutoring. Chat with us or submit request at [email protected]
Theory and lecture notes of Quadratic Functions all along with the key concepts of quadratic functions, standard form, Extrema-Maximum and Minimums, Absolute Minimum, Absolute Maximum, Constant function and Quartic function. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Quadratic Functions.
Insulating materials are exists in dissimilar shapes and sizes. Insulating materials are presented like Tapes, rolls, sleeves, paper and cloth.
Interactions in an Ecosystem tutorial all along with the key concepts of Competition, Predation, Parasitism, Symbiosis, Commensalism and Saprophytism
The meaning of joint products is two or more products generates intentionally and with similar inputs and containing more or less similar economic value.
Vinegar Analysis and Chromatography tutorial all along with the key concepts of Description of chromatography, Types of Chromatography, Gas chromatography, Chromatography Work, Theory of Thin Layer Chromatography, Experimental procedure
Oxidation Reduction Titration tutorial all along with the key concepts of Electrochemical cell, Redox Titration Curve, Detecting Redox End Point, Iodimetry and Iodometry
Theory and lecture notes of Arithmetic Sequences all along with the key concepts of arithmetic sequences, Partial Sum of an Arithmetic Sequence, Common Difference and General Term of Arithmetic Sequences. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Arithmetic Sequences.
Theory and lecture notes of How a Fixed Exchange Rate System Works all along with the key concepts of High Capital Mobility, Barriers to Capital Mobility, Limited Capital Mobility, Choice of Exchange Rate Systems. Tutorsglobe offers homework help, assignment help and tutor’s assistance on How a Fixed Exchange Rate System Works.
it is a natural system of classification and is relies on significant characters of the plants. yet today this system is being followed in united kingdom (uk) and various other commonwealth countries.
www.tutorsglobe.com offers synthetic preparation homework help, synthetic preparation assignment help, online tutoring assistance, organic chemistry solutions by online qualified tutor's help.
www.tutorsglobe.com offers Concept of Abstraction homework help, assignment help, case study, writing homework help, online tutoring assistance by computer science tutors.
tutorsglobe.com intermolecular forces assignment help-homework help by online atomic structure tutors
Theory and lecture notes of Stock Market and Interest Rates all along with the key concepts of stock market and interest rates, Stock Market, Interest Rates. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Stock Market and Interest Rates.
tutorsglobe.com gender in work and society assignment help-homework help by online humanities tutors
while electric supply is provided to the heating element by using 3-core power cord, the heat generated in the element will be transferred to the sole-plate that is then pressed over the cloth to be ironed.
1933877
Questions Asked
3689
Tutors
1460905
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!