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

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Linear Energy Transfer is the rate of energy loss per unit length of matter. Check FAQs

LET = \frac{4 \cdot π \cdot z^{2} \cdot e^{4}}{m e \cdot v^{2}} \cdot [Avaga-no] \cdot \frac{ρ}{A} \cdot (\ln (\frac{2 \cdot m e \cdot v^{2}}{I}) - \ln (1 - β^{2}) - β^{2})

LET - Linear Energy Transfer?z - Charge of moving particle?e - Charge of Electron?m_e - Mass of Electron?v - Velocity of moving particle?ρ - Density of Stopping Matter?A - Atomic Weight of Stopping Matter?I - Mean Excitation Energy of Stopping Matter?β - Ratio of Particle Velocity to that of Light?[Avaga-no] - Avogadro’s number?π - Archimedes' constant?

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

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Here is how the Bethe's Equation for LET for Charged Particles due to Collisions with Electrons equation looks like with Values.

Here is how the Bethe's Equation for LET for Charged Particles due to Collisions with Electrons equation looks like with Units.

Here is how the Bethe's Equation for LET for Charged Particles due to Collisions with Electrons equation looks like.

-18508200.4966 = \frac{4 \cdot 3.1416 \cdot 2^{2} \cdot {4.8E-10}^{4}}{9.1E-28 \cdot {2E-8}^{2}} \cdot 6E+23 \cdot \frac{2.32}{4.7E-23} \cdot (\ln (\frac{2 \cdot 9.1E-28 \cdot {2E-8}^{2}}{30}) - \ln (1 - {0.067}^{2}) - {0.067}^{2})

-18508200.4966N = \frac{4 \cdot 3.1416 \cdot {2ESU of Charge}^{2} \cdot {4.8E-10ESU of Charge}^{4}}{9.1E-28g \cdot {2E-8m/s}^{2}} \cdot 6E+23 \cdot \frac{2.32g/cm³}{4.7E-23g} \cdot (\ln (\frac{2 \cdot 9.1E-28g \cdot {2E-8m/s}^{2}}{30eV}) - \ln (1 - {0.067}^{2}) - {0.067}^{2})

-18508200.4966 = \frac{4 \cdot 3.1416 \cdot 2^{2} \cdot {4.8E-10}^{4}}{9.1E-28 \cdot {2E-8}^{2}} \cdot 6E+23 \cdot \frac{2.32}{4.7E-23} \cdot (\ln (\frac{2 \cdot 9.1E-28 \cdot {2E-8}^{2}}{30}) - \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

Follow our step by step solution on how to calculate Bethe's Equation for LET for Charged Particles due to Collisions with Electrons?

FIRST Step Consider the formula

LET = \frac{4 \cdot π \cdot z^{2} \cdot e^{4}}{m e \cdot v^{2}} \cdot [Avaga-no] \cdot \frac{ρ}{A} \cdot (\ln (\frac{2 \cdot m e \cdot v^{2}}{I}) - \ln (1 - β^{2}) - β^{2})

Next Step Substitute values of Variables

∴

LET = \frac{4 \cdot π \cdot {2ESU of Charge}^{2} \cdot {4.8E-10ESU of Charge}^{4}}{9.1E-28g \cdot {2E-8m/s}^{2}} \cdot [Avaga-no] \cdot \frac{2.32g/cm³}{4.7E-23g} \cdot (\ln (\frac{2 \cdot 9.1E-28g \cdot {2E-8m/s}^{2}}{30eV}) - \ln (1 - {0.067}^{2}) - {0.067}^{2})

Next Step Substitute values of Constants

∴

LET = \frac{4 \cdot 3.1416 \cdot {2ESU of Charge}^{2} \cdot {4.8E-10ESU of Charge}^{4}}{9.1E-28g \cdot {2E-8m/s}^{2}} \cdot 6E+23 \cdot \frac{2.32g/cm³}{4.7E-23g} \cdot (\ln (\frac{2 \cdot 9.1E-28g \cdot {2E-8m/s}^{2}}{30eV}) - \ln (1 - {0.067}^{2}) - {0.067}^{2})

Next Step Convert Units

∴

LET = \frac{4 \cdot 3.1416 \cdot {6.7E-10C}^{2} \cdot {1.6E-19C}^{4}}{9.1E-31kg \cdot {2E-8m/s}^{2}} \cdot 6E+23 \cdot \frac{2320kg/m³}{4.7E-26kg} \cdot (\ln (\frac{2 \cdot 9.1E-31kg \cdot {2E-8m/s}^{2}}{4.8E-18J}) - \ln (1 - {0.067}^{2}) - {0.067}^{2})

Next Step Prepare to Evaluate

∴

LET = \frac{4 \cdot 3.1416 \cdot {6.7E-10}^{2} \cdot {1.6E-19}^{4}}{9.1E-31 \cdot {2E-8}^{2}} \cdot 6E+23 \cdot \frac{2320}{4.7E-26} \cdot (\ln (\frac{2 \cdot 9.1E-31 \cdot {2E-8}^{2}}{4.8E-18}) - \ln (1 - {0.067}^{2}) - {0.067}^{2})

Next Step Evaluate

∴

LET = -18508200.4966457N

LAST Step Rounding Answer

∴

LET = -18508200.4966N

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

Variables

Constants

Functions

Linear Energy Transfer

Linear Energy Transfer is the rate of energy loss per unit length of matter.

Symbol: LET

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Linear Energy Transfer

Charge of moving particle

Charge of moving particle is the electric charge that a moving particle carries.

Symbol: z

Measurement: Electric ChargeUnit: ESU of Charge

Note: Value can be positive or negative.

Formulas to find Charge of moving particle

Charge of Electron

Charge of Electron is the amount of electrical charge carried by an electron.

Symbol: e

Measurement: Electric ChargeUnit: ESU of Charge

Note: Value can be positive or negative.

Formulas to find Charge of Electron

Mass of Electron

Mass of Electron is the weight of a single electron.

Symbol: m_e

Measurement: WeightUnit: g

Note: Value can be positive or negative.

Formulas to find Mass of Electron

Velocity of moving particle

Velocity of moving particle is defined as the speed in which a charged particles moves.

Symbol: v

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Velocity of moving particle

Density of Stopping Matter

Density of Stopping Matter is the measurement of how tightly the stopping matter is packed together.

Symbol: ρ

Measurement: DensityUnit: g/cm³

Note: Value can be positive or negative.

Formulas to find Density of Stopping Matter

Atomic Weight of Stopping Matter

Atomic Weight of Stopping Matter is the weight of the matter that stop a particle moving at velocity v.

Symbol: A

Measurement: WeightUnit: g

Note: Value can be positive or negative.

Formulas to find Atomic Weight of Stopping Matter

Mean Excitation Energy of Stopping Matter

Mean Excitation Energy of Stopping Matter is the ionization energy of the stopping matter. It is almost equal to 30eV.

Symbol: I

Measurement: EnergyUnit: eV

Note: Value can be positive or negative.

Formulas to find Mean Excitation Energy of Stopping Matter

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.

Symbol: β

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Ratio of Particle Velocity to that of Light

Avogadro’s number

Avogadro’s number represents the number of entities (atoms, molecules, ions, etc.) in one mole of a substance.

Symbol: [Avaga-no]

Value: 6.02214076E+23

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other formulas in Nuclear Chemistry category

Go Binding Energy Per Nucleon

B.E per nucleon = \frac{∆m \cdot 931.5}{A}

Go Mean Life Time

ζ = 1.446 \cdot T 1/2

How to Evaluate 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 evaluator 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 evaluate 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 evaluate Bethe's Equation for LET for Charged Particles due to Collisions with Electrons using this online evaluator? To use this online evaluator 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.

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

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

The formula of Bethe's Equation for LET for Charged Particles due to Collisions with Electrons is expressed as 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). Here is an example- -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).

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

With 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) we can find Bethe's Equation for LET for Charged Particles due to Collisions with Electrons using the formula - 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). This formula also uses Avogadro’s number, Archimedes' constant and Natural Logarithm (ln) function(s).

Can the Bethe's Equation for LET for Charged Particles due to Collisions with Electrons be negative?

Yes, the Bethe's Equation for LET for Charged Particles due to Collisions with Electrons, measured in Force can be negative.

Which unit is used to measure 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 is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Bethe's Equation for LET for Charged Particles due to Collisions with Electrons can be measured.

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

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

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

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

Other formulas in Nuclear Chemistry category

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

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

Variable Name