Bethe's Equation for LET for Charged Particles due to Collisions with Electrons Calculator

✖Charge of moving particle is the electric charge that a moving particle carries.ⓘ Charge of moving particle [z]			+10% -10%
✖Charge of Electron is the amount of electrical charge carried by an electron.ⓘ Charge of Electron [e]			+10% -10%
✖Mass of Electron is the weight of a single electron.ⓘ Mass of Electron [m_e]			+10% -10%
✖Velocity of moving particle is defined as the speed in which a charged particles moves.ⓘ Velocity of moving particle [v]			+10% -10%
✖Density of Stopping Matter is the measurement of how tightly the stopping matter is packed together.ⓘ Density of Stopping Matter [ρ]			+10% -10%
✖Atomic Weight of Stopping Matter is the weight of the matter that stop a particle moving at velocity v.ⓘ Atomic Weight of Stopping Matter [A]			+10% -10%
✖Mean Excitation Energy of Stopping Matter is the ionization energy of the stopping matter. It is almost equal to 30eV.ⓘ Mean Excitation Energy of Stopping Matter [I]			+10% -10%
✖Ratio of Particle Velocity to that of Light is the quantitative relationship between the velocity of the moving particle to that of light.ⓘ Ratio of Particle Velocity to that of Light [β]			+10% -10%

✖Linear Energy Transfer is the rate of energy loss per unit length of matter.ⓘ Bethe's Equation for LET for Charged Particles due to Collisions with Electrons [LET]

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Bethe's Equation for LET for Charged Particles due to Collisions with Electrons

Formula

`"LET" = (4*pi*"z"^2*"e"^4)/("m"_{"e"}*"v"^2)*"[Avaga-no]"*"ρ"/"A"*(ln((2*"m"_{"e"}*"v"^2)/"I")-ln(1-"β"^2)-"β"^2)`

Example

`"-18508200.496646N"=(4*pi*("2ESU of Charge")^2*("4.8E^-10ESU of Charge")^4)/("9.1096E^-28g"*("2.0454E^-8m/s")^2)*"[Avaga-no]"*"2.32g/cm³"/"4.66E^-23g"*(ln((2*"9.1096E^-28g"*("2.0454E^-8m/s")^2)/"30eV")-ln(1-("0.067")^2)-("0.067")^2)`

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Bethe's Equation for LET for Charged Particles due to Collisions with Electrons Solution

STEP 0: Pre-Calculation Summary

Formula Used

Linear Energy Transfer = (4*pi*Charge of moving particle^2*Charge of Electron^4)/(Mass of Electron*Velocity of moving particle^2)*[Avaga-no]*Density of Stopping Matter/Atomic Weight of Stopping Matter*(ln((2*Mass of Electron*Velocity of moving particle^2)/Mean Excitation Energy of Stopping Matter)-ln(1-Ratio of Particle Velocity to that of Light^2)-Ratio of Particle Velocity to that of Light^2)
LET = (4*pi*z^2*e^4)/(m_e*v^2)*[Avaga-no]*ρ/A*(ln((2*m_e*v^2)/I)-ln(1-β^2)-β^2)
This formula uses 2 Constants, 1 Functions, 9 Variables

Constants Used

[Avaga-no] - Avogadro’s number Value Taken As 6.02214076E+23
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Linear Energy Transfer - (Measured in Newton) - Linear Energy Transfer is the rate of energy loss per unit length of matter.
Charge of moving particle - (Measured in Coulomb) - Charge of moving particle is the electric charge that a moving particle carries.
Charge of Electron - (Measured in Coulomb) - Charge of Electron is the amount of electrical charge carried by an electron.
Mass of Electron - (Measured in Kilogram) - Mass of Electron is the weight of a single electron.
Velocity of moving particle - (Measured in Meter per Second) - Velocity of moving particle is defined as the speed in which a charged particles moves.
Density of Stopping Matter - (Measured in Kilogram per Cubic Meter) - Density of Stopping Matter is the measurement of how tightly the stopping matter is packed together.
Atomic Weight of Stopping Matter - (Measured in Kilogram) - Atomic Weight of Stopping Matter is the weight of the matter that stop a particle moving at velocity v.
Mean Excitation Energy of Stopping Matter - (Measured in Joule) - Mean Excitation Energy of Stopping Matter is the ionization energy of the stopping matter. It is almost equal to 30eV.
Ratio of Particle Velocity to that of Light - Ratio of Particle Velocity to that of Light is the quantitative relationship between the velocity of the moving particle to that of light.

STEP 1: Convert Input(s) to Base Unit

Charge of moving particle: 2 ESU of Charge --> 6.67128190396304E-10 Coulomb (Check conversion here)
Charge of Electron: 4.8E-10 ESU of Charge --> 1.60110765695113E-19 Coulomb (Check conversion here)
Mass of Electron: 9.1096E-28 Gram --> 9.1096E-31 Kilogram (Check conversion here)
Velocity of moving particle: 2.0454E-08 Meter per Second --> 2.0454E-08 Meter per Second No Conversion Required
Density of Stopping Matter: 2.32 Gram per Cubic Centimeter --> 2320 Kilogram per Cubic Meter (Check conversion here)
Atomic Weight of Stopping Matter: 4.66E-23 Gram --> 4.66E-26 Kilogram (Check conversion here)
Mean Excitation Energy of Stopping Matter: 30 Electron-Volt --> 4.80653199000002E-18 Joule (Check conversion here)
Ratio of Particle Velocity to that of Light: 0.067 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

LET = (4*pi*z^2*e^4)/(m_e*v^2)*[Avaga-no]*ρ/A*(ln((2*m_e*v^2)/I)-ln(1-β^2)-β^2) --> (4*pi*6.67128190396304E-10^2*1.60110765695113E-19^4)/(9.1096E-31*2.0454E-08^2)*[Avaga-no]*2320/4.66E-26*(ln((2*9.1096E-31*2.0454E-08^2)/4.80653199000002E-18)-ln(1-0.067^2)-0.067^2)

Evaluating ... ...

LET = -18508200.4966457

STEP 3: Convert Result to Output's Unit

-18508200.4966457 Newton --> No Conversion Required

FINAL ANSWER

-18508200.4966457 ≈ -18508200.496646 Newton <-- Linear Energy Transfer

(Calculation completed in 00.004 seconds)

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Bethe's Equation for LET for Charged Particles due to Collisions with Electrons Formula

What is Linear Energy Transfer?

In dosimetry, linear energy transfer (LET) is the amount of energy that an ionizing particle transfers to the material traversed per unit distance. It describes the action of radiation into matter.
It is identical to the retarding force acting on a charged ionizing particle travelling through the matter.[1] By definition, LET is a positive quantity. LET depends on the nature of the radiation as well as on the material traversed. Linear energy transfer is closely related to stopping power, since both equal the retarding force. The unrestricted linear energy transfer is identical to linear electronic stopping power.
The appropriate SI unit for LET is the newton, but it is most typically expressed in units of kiloelectronvolts per micrometre (keV/μm) or megaelectronvolts per centimetre (MeV/cm).

How to Calculate Bethe's Equation for LET for Charged Particles due to Collisions with Electrons?

Bethe's Equation for LET for Charged Particles due to Collisions with Electrons calculator uses Linear Energy Transfer = (4*pi*Charge of moving particle^2*Charge of Electron^4)/(Mass of Electron*Velocity of moving particle^2)*[Avaga-no]*Density of Stopping Matter/Atomic Weight of Stopping Matter*(ln((2*Mass of Electron*Velocity of moving particle^2)/Mean Excitation Energy of Stopping Matter)-ln(1-Ratio of Particle Velocity to that of Light^2)-Ratio of Particle Velocity to that of Light^2) to calculate the Linear Energy Transfer, The Bethe's Equation for LET for Charged Particles due to Collisions with Electrons formula is defined as the rate of energy loss per unit of length. Linear Energy Transfer is denoted by LET symbol.

How to calculate Bethe's Equation for LET for Charged Particles due to Collisions with Electrons using this online calculator? To use this online calculator for Bethe's Equation for LET for Charged Particles due to Collisions with Electrons, enter Charge of moving particle (z), Charge of Electron (e), Mass of Electron (m_e), Velocity of moving particle (v), Density of Stopping Matter (ρ), Atomic Weight of Stopping Matter (A), Mean Excitation Energy of Stopping Matter (I) & Ratio of Particle Velocity to that of Light (β) and hit the calculate button. Here is how the Bethe's Equation for LET for Charged Particles due to Collisions with Electrons calculation can be explained with given input values -> -18508188.864544 = (4*pi*6.67128190396304E-10^2*1.60110765695113E-19^4)/(9.1096E-31*2.0454E-08^2)*[Avaga-no]*2320/4.66E-26*(ln((2*9.1096E-31*2.0454E-08^2)/4.80653199000002E-18)-ln(1-0.067^2)-0.067^2).

FAQ

What is Bethe's Equation for LET for Charged Particles due to Collisions with Electrons?

The Bethe's Equation for LET for Charged Particles due to Collisions with Electrons formula is defined as the rate of energy loss per unit of length and is represented as LET = (4*pi*z^2*e^4)/(m_e*v^2)*[Avaga-no]*ρ/A*(ln((2*m_e*v^2)/I)-ln(1-β^2)-β^2) or Linear Energy Transfer = (4*pi*Charge of moving particle^2*Charge of Electron^4)/(Mass of Electron*Velocity of moving particle^2)*[Avaga-no]*Density of Stopping Matter/Atomic Weight of Stopping Matter*(ln((2*Mass of Electron*Velocity of moving particle^2)/Mean Excitation Energy of Stopping Matter)-ln(1-Ratio of Particle Velocity to that of Light^2)-Ratio of Particle Velocity to that of Light^2). Charge of moving particle is the electric charge that a moving particle carries, Charge of Electron is the amount of electrical charge carried by an electron, Mass of Electron is the weight of a single electron, Velocity of moving particle is defined as the speed in which a charged particles moves, Density of Stopping Matter is the measurement of how tightly the stopping matter is packed together, Atomic Weight of Stopping Matter is the weight of the matter that stop a particle moving at velocity v, Mean Excitation Energy of Stopping Matter is the ionization energy of the stopping matter. It is almost equal to 30eV & Ratio of Particle Velocity to that of Light is the quantitative relationship between the velocity of the moving particle to that of light.

How to calculate Bethe's Equation for LET for Charged Particles due to Collisions with Electrons?

The Bethe's Equation for LET for Charged Particles due to Collisions with Electrons formula is defined as the rate of energy loss per unit of length is calculated using Linear Energy Transfer = (4*pi*Charge of moving particle^2*Charge of Electron^4)/(Mass of Electron*Velocity of moving particle^2)*[Avaga-no]*Density of Stopping Matter/Atomic Weight of Stopping Matter*(ln((2*Mass of Electron*Velocity of moving particle^2)/Mean Excitation Energy of Stopping Matter)-ln(1-Ratio of Particle Velocity to that of Light^2)-Ratio of Particle Velocity to that of Light^2). To calculate Bethe's Equation for LET for Charged Particles due to Collisions with Electrons, you need Charge of moving particle (z), Charge of Electron (e), Mass of Electron (m_e), Velocity of moving particle (v), Density of Stopping Matter (ρ), Atomic Weight of Stopping Matter (A), Mean Excitation Energy of Stopping Matter (I) & Ratio of Particle Velocity to that of Light (β). With our tool, you need to enter the respective value for Charge of moving particle, Charge of Electron, Mass of Electron, Velocity of moving particle, Density of Stopping Matter, Atomic Weight of Stopping Matter, Mean Excitation Energy of Stopping Matter & Ratio of Particle Velocity to that of Light and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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