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# Beta

Beta particles are highly energetic and fast electrons or positrons that are emitted by certain types of radioactive nuclei. Beta particles that are emitted are a form of ionizing radiation known as beta rays. There are two forms of beta particles, ÃŸ+ or ÃŸ-, depending on if it is a positron or electron respectively.

ÃŸ- Decay or electron emission, is an unstable atomic nucleus with an excess of neutrons where the neutrons are converted into a proton, an electron and an electron-type antineutrino. Below is the process by the weak interaction.

n â†’ p + eâˆ’ + Î½e

Beta decay mostly occurs with neutron-rich fission by products produced in nuclear reactors. Free neutrons will also decay by this process.
ÃŸ+ Decay or positron emission is an unstable atomic nucleus with an excess of protons where protons are converted into neutrons, a positron and an electron-type neutrino. Below is the process.

p â†’ n + e+ + Î½e

Beta plus decay will only happen inside a nucleus when the absolute value of the binding energy of the daughter nucleus is greater than that of the motherâ€™s nucleus. Therefore the daughter nucleus is a lower energy state.

Beta particles are used to treat many health conditions such as eye and bone cancers. Beta particles are also used in quality control testing of thickness of materials. They are also used in positron emission tomography, PET scans.

### Radioactive Decay and Beta Particles

C[14~6] is a pure beta emitter that decays to N[14~7]. If the exact atomic mass of the parent and daughter are 14.003242 amu and 14.003074 amu, respectively, calculate the energy of the most energetic beta particle.

### Hamiltonian Spin

Please assist me in solving the following problems: Let's consider an ion (in an effective spin state corresponding to s = 1) at a crystal lattice site. As for the effective potential seen by the ion, assume spin Hamiltonian of the form: H = alpha*S^2_z + beta*(S^2_z - S^2_y) where alpha and beta are some real con

### Relativistic Error in Classical Formula for Kinetic Energy

Using the classical and relativistic expressions for kinetic energy, calculate the range of velocities for a particle of mass m such that we use the classical expression for kinetic energy to within an accuracy of 1%.

### Problems in Statistical Mechanics

Please see the attachment for the formatted problem. 3. Consider again the lattice of N spin-1/2 particles in an external homogeneous magnetic field, where each particle has two possible states: spin "down" with energy e = 0 and spin "up" with energy e = 1/2". The microstate of the system is specified by the energy states of

What are the atomic number and mass number when: A. An isotope of atomic number 90 and mass number of 232 emits an alpha particle? B. An isotope of atomic number 48 and a mass number of 113 emits a beta particle?

### Volumetric expansion

A pyrex cooking pot of volume 2.5 liters is filled to the brim with water at room temperature of 22 degrees Celcius. How much water will spill out when both the pot and the water are heated to a temperaure of 80 degrees Celcius? Give your answer in Milliliters. beta of pyrex is .000009 per degree Celsius and beta of water is .00

### Atomic Nuclear Decay & Radioactivity in Healthcare.

1. Discuss in detail, one way in which atomic nuclear decay takes place. What is the significance of atomic nuclear decay? Analyze the societal implications of using this process. 2.What are the various uses of radioactivity in healthcare? What are the future trends in healthcare with respect to the use of radioactivity?

### Which of the statements are true about nuclear decays and radioactivity?

Which of the following statements are true about nuclear decays and radioactivity? True False a neutrino is a particle with a negative charge and a very small mass True False alpha decay involves emission of a 4He nucleus True False beta decay involves emission of an electron True False gamma decay involves e

### Physics: Calculate Coefficient of the Volume Expansion

During an all night cram session, a student heats up a one-half liter (0.50x10^-3b^3) glass (pyrex) beaker of cold coffee. Initaially, the temperature is 18 degrees celsius and the beaker is filled to the brim. A short time later when the student returns, the temperature is 92 degrees celsius. The coefficient of the volume expan

### Nuclear Reactions and Equations

Please see the attached file for the entire questions. Alpha, Beta, and Gamma Emitters When unstable nuclei decay, they generally decay into a more stable form. In the process, they emit radiation in the form of particles, particles, or rays. ? An Alpha particle is a helium nucleus, the symbol for which is . ? A

### Electromagnetism: Force on moving charges in magnetic field.

A beta particle (high-speed electron) is traveling at right angles to a 0.43 T magnetic field. It has a speed of 2.5 107 m/s. What size force acts on the particle? ------ A magnetic field of 27 T acts in a direction due west. An electron is traveling due south at 7.0 105 m/s. What are the magnitude and direction of the for

### Internal Energy for Nonrelativistic and Relativistic Gasses

(i) Show that the equation of state of an ideal gas is still PV = RT even when the gas is heated to such a high temperature that the particles are moving at relativistic speeds. (Hint: What feature of the partition function of the ideal gas determines the gas law?). (ii) Although the equation of state does not alter when the

### Internal Energy of N Anharmonic Oscillators

A system is composed of N one dimensional classical oscillators. Assume that the potential for the oscillators contains a small quartic "anharmonic" term V(x) = (m*Î©^2)/2 + a*x^4 Where a*(x^4) <<< KB T and (x^4) = average value Calculate the average energy per oscillator to the first order in a

### Parallel Transport of a Vector.

Solve the parallel transport equations for a vector v = (v^r, v^theta) being transported around a circle of radius a about r = 0 in the 2D space with the metric ds^2 = dr^2 + (1 - beta)r^2 dtheta^2 where beta is a constant. Use the parametrization of the circle with theta, 0 <= theta <= 2pi.

### Oscillations

Oscillations. See attached file for full problem description. 1) An undamped oscillator has period tau_0 = 1.000s, but I now add a little damping so that its period changes to tau1 = 1.001s. What is the damping factor Beta? By what factor will the amplitude of oscillation decrease after 10 cycles? Which effect of damping woul

### Partition functions and probability.

Imagine a particle that can be in only 3 states with energies 1 eV, 2 eV, and 3 eV. The particle is in equilibrium with a reservoir at 300 K. a) Calculate the partition function for this particle. b) Calculate the probability of the particle being in the 2 eV state. c) How does the probability in part (b) change if t

### Partition functions of boxes containing bosons, fermions, or distinguishable particles.

Suppose you have a "box" in which each particle may occupy any of 10 single-particle states. For simplicity, assume that each of these states has energy zero. (a) What is the partition function of this system if the box contains only one particle? (b) What is the partition function of this system if the box contains two dis

### Pressure of Ideal Bose and Fermi Gas Satisfy PV = 2/3 E

In class we wrote down the thermodynamical potential for a gas of non-interacting (non- relativistic) fermions in three dimensions. We found a simple result for fermions of the form (see attached).

### Expansion coefficient and the Lennard-Jones potential.

Consider a classical particle moving in a one-dimensional potential well u(x). The particle is in thermal equilibrium with a reservoir at temperature T, so the probabilities of its various states are determined by Boltzmann statistics. (a) Show that the average position of the particle is given by x =&#8747;xe-&#946;u(x)

### Fission and Quantum Theory

Uranium 238 can absorb a neutron and fission into two pieces. Identify the nucleus missing the the reaction in the attached file. Describe the resultant nucleus in each of the following reactions: (see attachment for reactions) What was Louis de Broglie's main contribution to quantum theory?

### Center of mass 10.26

A Ball Rolling Uphill. A bowling ball rolls without slipping up a ramp that slopes upward at an angle beta (B) to the horizontal. Treat the ball as a uniform, solid sphere, ignoring the finger holes. 1. What is the acceleration of the center of mass of the ball? 2. What minimum coefficient of static friction is needed to pre

A radioactive source in the form of a metallic sphere of radius 10^-2 m emits beta particles at the rate of 10^10 particles per second. The source is electrically insulated. What is the time required for its potential to be raised by 4 V assuming 50% of the emitted beta particles escape the source ?

### Distance Costs Decibels

(See attached file for full problem description) --- Distance Costs Decibels The general formula for the number of decibels corresponding to a change in sound intensity to relative to the former intensity is Part A Suppose that a sound has initial intensity measured in decibels. This sound now increases in intensi

### Oscillations

Assume you are looking at a top view of an object of mass m connected between 2 stretched rubber bands of length L. The objects rests on a frictionless surface. At equilibrium, the tension in each rubber band is T. Find an expression for the frequency of oscillations perpendicular to the rubber bands. Assume the amplitude is suf

### Calculating Nuclear Decay

I'm completely stuck on this problem: i) Determine the energy required to remove a proton from a 12C nucleus (in MeV) - For this one, I know that this is not alpha, beta, or gamma decay, so I don't know how I'm supposed to do it. And this one, ii) 2H and 3H nuclei undergo the following fission reaction: 2H + 3H --> 4He

### P 3.18 + 3.23 from 'Intro Elementary Particles' by Griffiths

See attached file for full problem description. 3.18 (a) A pion at rest decays into a muon and a neutrino (pi^- --> mu^- + V_mu). On the average, how far will the muon travel (in vacuum) before disintegrating? (b) The length of the muon track in Figure 1.7 is about 0.6 mm (the photograph has been enlarged). How do you expl

### How many Beta particles will be emitted in one minute

Please give step by step instructions on how to solve problem as detailed as posssible. I

### Alpha & Beta Penetration

a) How much energy does an alpha particle require to penetrate the minimal protective epidermal layer of skin (thickness~7mg/cm^2)? b) How much energy does an beta particle require to penetrate the minimal protective epidermal layer of skin (thickness~7mg/cm^2)?

### Beta Identification

You are a health physicist and you find an unknown contaminant that proves to be a pure beta emitter. To try to identify the contaminant, you attempt to determine the maximum energy of the beta rays. You use a GM tube with a thin (0.1 mm, ?=2.7 g/cm^3) end window. You find that 1.74 mm stops all of the beta particles. The distan