A. Who first discovered radioactivity?

B. In what year did he discover it?

A radioactive nucleus has excess energy, which is constantly being redistributed among the nucleons by mutual collisions.  By probability, one of the nucleons (or a byproduct of the decay of a nucleon) will gain enough energy to escape the nucleus.

This escaping particle is called radiation.

Radiation will continue until the nucleus reaches its ground state (becomes stable).

ΔN/Δt = -λN

ΔN = the change in number of radioactive nuclei per unit time, Δt.

λ = decay constant

N = number of radioactive nuclei present

Solving for the differential equation dN/dt = -λN:

N = N₀e^-λt

A. What is activity?

B. What is the SI unit for activity?

C. What formula describes activity?

A. Activity is the rate of decay of a radioactive nuclide.

B. The SI unit for activity is the becquerel, Bq.

1 Bq = 1 dps

C. A = ΔN/Δt = -λN

A = A₀e^-λt

A. Besides the SI unit, what is another unit of activity?

B. How was this unit traditionally defined?

A. Another unit of activity is the curie, Ci.

B. The curie was traditionally defined as the activity of 1g of radium.  However, the activity of 1g of radium has been more accurately measured to be 0.976 Ci (3.61 x 10¹⁰ Bq)

A. What is 'half-life'?

B. What is the symbol for half-life?

B. Derive the formula for half-life.

A. Half-life is defined as the time required for a population of radioactive nuclides to decay to one-half its original value.

B. T_1/2

C. N = N₀e^-λt

N₀ = 2N

1/2 = e^-λt

ln(1/2) = ln(e^-λt)

-0.693 = -λT_1/2

T_1/2 = 0.693/λ

A. What is mean life?

B. What is mean life also known as?

C. How can mean life also be understood?

D. What is the symbol for mean life?

E. What is the relationship between mean life and half-life?

A. Mean life is the average lifetime of a radioactive nucleus.  

B. Mean life is also known as Average life.

C. Mean life can be understood by considering an imaginary source that decays at a constant rate, regardless of N:  A = A₀.  The imaginary source produces the same number of total disintegrations as the real source decaying exponentially from t=0 to t=∞.  Thus, the mean life will be the total time it takes for all disintegrations to occur divided by the total number of disintegrations (N₀).

D. T_a

E. T_a = 1.44 T_1/2

ΔN/Δt = -λN

Because A = A₀, 

ΔN/Δt = -λN₀

ΔN = (-λN₀)Δt

Let ΔN = N₀ (ΔN is now in units of disintegrations; We must replace -λ with +λ):

N₀ = (λN₀₎t

There are N₀ disintegrations in time t,

T_a is the time it takes for 1 disintegration to occur (because we are assuming constant activity):

N₀/N₀ = λT_a

λT_a = 1

T_a = 1/λ = 1.44 T_1/2

1. Uranium series: ²³⁸₉₂U ----> ²⁰⁶₈₂Pb

    2. Actinium series: ²³⁵₉₂U ----> ²⁰⁷₈₂Pb

     3. Thorium series: ²³²₉₀Th ----> ²⁰⁸₈₂Pb

A. Define radioactive equilibrium.

B. Describe the two types of radioactive equilibrium.

A. Radioactive equilibrium is a state in which the ratio of activity between a radioactive parent and its radioactive daughter is achieved.

B. Transient Equilibrium: T_1/2,Parent > T_1/2,Daughter

A₂/A₁ = λ₂ / λ₂-λ₁ = T₁ / T₁-T₂

Ex: ⁹⁹₄₂Mo (T_1/2=67hr) --> ^99m₄₃Tc (T_1/2=6hr)

Secular Equilibrium: T_1/2,Parent >>> T_1/2,Daughter

A₂ = A₁

Ex: ²²⁶₈₈Ra (T_1/2=1622y) --> ²²²₈₆Rn (T_1/2=3.8d)

A. Describe the general reaction for α-particle decay.

B. When does α-particle decay most often occur and why?

C. What can be said about the kinetic energy of the emitted α-particle?

A.

_^AZX --> ^A-4_Z-2Y + ⁴₂He + Q

Ex: ²²⁶₈₈Ra (T_1/2=1622y) --> ²²²₈₆Rn + ⁴₂He + 4.87 MeV

B. α-particle decay most often occurs in radionuclides with Z > 82.  It occurs when the coulombic force of repulsion between protons is great enough to overcome the strong force.

C. α-particles are emitted with discrete energies specific to the parent nuclide.

A. What is disintegration energy?

B. Most of the disintegration energy is carried by ______?

A. Disintegration energy, Q, is the total energy released in radioactive decay.  It is equivalent to the difference between the mass of the parent nucleus and the sum of the masses of the products.  It appears as the kinetic energy of the products (recoil nucleus, emitted radiation).

B. Most of the disintegration energy is carried by the emitted particles (Because m_{recoil nucleus} >> m_{emitted particles})

1. Negatron emission (Β^- decay)

2. Positron emission (Β⁺ decay)

A. Describe the general reaction for Β^- decay.

B. When does Β^- decay occur?

A.

 ¹₀n ---> ¹₁p + ⁰_-1Β + v

^A_ZX ---> ^A_Z+1Y + ⁰_-1Β + v + Q  

Ex: ³²₁₅P (T_1/2=14.3d) ---> ³²₁₆S + ⁰_-1B + v + 1.7 MeV

* v = antineutrino

B. B^- occurs when N/P is too high (the nuclide lies above the region of stability)

1. The recoil nucleus- the daughter nucleus

2. Emitted particles (α, Β, γ, ν, etc)

A. Describe the general reaction for Β⁺ decay.

B. When does Β⁺ decay usually occur?

A.

¹₁p --> ¹₀n + ⁰₊₁Β + v + Q

^A_ZX --> ^A_Z-1Y + ⁰₊₁Β + v + Q

Ex: ²²₁₁Na --> ²²₁₀Ne + ⁰₊₁Β + v +Q

B. Β⁺ decay occurs when N/P is too low (the nuclide lies below the region of stability)

A. Is the spectrum of Β-particle energy discrete or continuous?

B. Why?

C. Who hypothesized the emission of a second particle in Β-decay and in what year?

A. The Β-particle energy spectrum is continuous.

B. The spectrum of Β-energies is continuous because more than one particle is emitted.  If only one were emitted, each would have E = Q and a sharp line spectrum would be seen.

C. Wolfgang Pauli hypothesized the emission of a second particle, the neutrino, in 1931.

A. Describe the general reaction for electron capture.

B. Electron capture is an alternative to ______.

C. What is the most common type of electron capture?

A.

¹₁p + ⁰_-1e --> ¹₀n + v + Q

^A_ZX + ⁰_-1e --> ^A_Z-1Y + v + Q

B. Electron capture is an alternative to Β⁺ decay.

C. K-capture is the most common type of electron capture.

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What type of radioactive equilibrium is this?

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What type of radioactive equilibrium is this?

A. If characteristic x-rays interact with orbital electrons, _____ can be produced.

B. This process is known as ______.

A. Auger electrons

B. Internal photoelectric effect

A. What is fluorescent yield?

B. What is its symbol?

C. What is its relationship with atomic number?

A. The emission of characteristic x-rays and the ejection of Auger electrons are competing processes.  The fluorescent yield is defined as the ratio of characteristic (fluorescent) x-rays to the number of electron shell vacancies.

B. ω

C. ω tends to increase with Z.

For low-Z materials, Auger electrons are favored.  As Z increases (Z > 30), characteristic x-rays are increasingly predominant.

Ex: Soft Tissue: ω ~ 0
Tungsten (Z = 74): ω ~0.93 

A. Describe the process of internal conversion.

B. What other process does internal conversion compete with?

A. Internal conversion is a process by which excess nuclear energy is passed on to an orbital electron, which is ejected.

B. Internal conversion competes with the direct emission of a γ-ray from the nucleus.

A. A daughter nuclide can be unstable, yet remain in this excited state for an appreciable amount of time before returning to its stable ground state.  When this happens, the excited state is known as ______.

B. When a nuclide of this type of excited state eventually returns to its ground state, the transformation is called ______.

A. the metastable state

B. an isomeric transition

A. What type of nuclear reaction is responsible for the contamination of high-energy x-ray beams from linear accelerators?

B. Describe this nuclear reaction.

C. At what photon energies does this process generally occur?

A. Photodisintegration

B. A high-energy photon interacts with an atomic nucleus, leading to the emission of one or more nucleons (n, p, d, t, α, etc.)

d = deuteron (²₁H)
t = triton (³₁H) 

C. >10 MeV