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Nuclear structure
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A = mass number, #nucleons

Z = #protons

A-Z = #neutrons


Characteristic photon energy (higher j shell to lower i shell)
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Eij = Ej - Ei


Ejected Auger electon energy
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Eijk = (Ei - Ej) - Ek

(Ejected electron from higher k shell as a result of a transition from the higher j shell to the lower i shell)


Half life
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t1/2 = ln2/λ = 0.693/λ

A(t) = A0e-λt

A(t) = A0e-((0.693 x given time)/half-life)

 A0 = A(t)e((0.693 x given time)/half-life)


Effective half-life
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Effective half-life denotes the halving of radioactive material in a living organism by means of radioactive decay and biological excretion.

{\lambda_e} \, = {\lambda_p} \, + {\lambda_b} \,

 t_{1/2} = \frac{\ln (2)}{\lambda_e}

 t_{e} = \frac{t_{p}\times t_{b}} {t_{p} + t_{b}}.


Mean/average life
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tavg = 1.44t1/2

Total dose = (initial dose rate)(time)(1.44)


Specific activity
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SA=A/M=λ·NA/AW

NA= avogadro's number

AW= atomic weight

λ = disintegration rate


Time required to reach a certain activity
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t=1.44·t1/2ln[A(t)/A0]


Brachy exposure rate calc
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X=ΓA/d2

Γ= gamma constant (R·cm2/mg·hr)

A= radionuclide activity

d= distance from source


mgRaEq --> mCi
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mgRaEq = (Γradionuclide/ Γradium)(# mCi of radionuclide)

 # mCi of radionuclide = (Γradium/ Γradionuclide)(mgRaEq)


Brachy PDD
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PDD = Dose at distance d from surface of cylinder/dose a surface of cylinder.


Inverse square
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I2/I1 = (r1/r2)2


Inverse square factor
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ISF = [(SSDcal+dmax)/(SSDtreat+dmax)]2


Mayneord F-factor
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Standard table of PDD are usually generated at the calibration SSD.  It is sometimes necessary to increase the SSD in order to treat a large field.  Since PDD is dependent on SSD, thistable of PDD will not be correct for the new SSD.  The Mayneord F-factor five the PDD at the new SSD.

F={[(SSD2+dmax)/(SSD1+dmax)][(SSD1+d)/(SSD2+d)]}2

Mayneords F overestimates PDD at large SSD's.


PDD at different SSD's
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PDDSSD2=

PDDSSD1[(SSD1+d)(SSD2+dmax)/(SSD2+d)(SSD1+dmax)]2