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Distance of closest approach Formula

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Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus. Check FAQs

r 0 = \frac{[Coulomb] \cdot 4 \cdot Z \cdot ({[Charge-e]}^{2})}{[Atomic-m] \cdot (v^{2})}

r₀ - Distance of Closest Approach?Z - Atomic Number?v - Velocity of alpha particle?[Coulomb] - Coulomb constant?[Charge-e] - Charge of electron?[Atomic-m] - Atomic mass unit?

Distance of closest approach Example

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Here is how the Distance of closest approach equation looks like with Values.

Here is how the Distance of closest approach equation looks like with Units.

Here is how the Distance of closest approach equation looks like.

2.4E+9 = \frac{9E+9 \cdot 4 \cdot 17 \cdot ({1.6E-19}^{2})}{1.7E-27 \cdot ({6.34}^{2})}

2.4E+9A = \frac{9E+9 \cdot 4 \cdot 17 \cdot ({1.6E-19C}^{2})}{1.7E-27kg \cdot ({6.34m/s}^{2})}

2.4E+9 = \frac{9E+9 \cdot 4 \cdot 17 \cdot ({1.6E-19}^{2})}{1.7E-27 \cdot ({6.34}^{2})}

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Distance of closest approach Solution

Follow our step by step solution on how to calculate Distance of closest approach?

FIRST Step Consider the formula

r 0 = \frac{[Coulomb] \cdot 4 \cdot Z \cdot ({[Charge-e]}^{2})}{[Atomic-m] \cdot (v^{2})}

Next Step Substitute values of Variables

∴

r 0 = \frac{[Coulomb] \cdot 4 \cdot 17 \cdot ({[Charge-e]}^{2})}{[Atomic-m] \cdot ({6.34m/s}^{2})}

Next Step Substitute values of Constants

∴

r 0 = \frac{9E+9 \cdot 4 \cdot 17 \cdot ({1.6E-19C}^{2})}{1.7E-27kg \cdot ({6.34m/s}^{2})}

Next Step Prepare to Evaluate

∴

r 0 = \frac{9E+9 \cdot 4 \cdot 17 \cdot ({1.6E-19}^{2})}{1.7E-27 \cdot ({6.34}^{2})}

Next Step Evaluate

∴

r 0 = 0.23504079171485m

Next Step Convert to Output's Unit

∴

r 0 = 2350407917.1485A

LAST Step Rounding Answer

∴

r 0 = 2.4E+9A

Distance of closest approach Formula Elements

Variables

Constants

Distance of Closest Approach

Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus.

Symbol: r₀

Measurement: LengthUnit: A

Note: Value can be positive or negative.

Formulas to find Distance of Closest Approach

Atomic Number

Atomic Number is the number of protons present inside the nucleus of an atom of an element.

Symbol: Z

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Atomic Number

Velocity of alpha particle

Velocity of alpha particle is a vector quantity (it has both magnitude and direction), and is the time rate of change of position (of a particle).

Symbol: v

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Velocity of alpha particle

Coulomb constant

Coulomb constant appears in Coulomb's law and quantifies the electrostatic force between two point charges. It plays a fundamental role in the study of electrostatics.

Symbol: [Coulomb]

Value: 8.9875E+9

Charge of electron

Charge of electron is a fundamental physical constant, representing the electric charge carried by an electron, which is the elementary particle with a negative electric charge.

Symbol: [Charge-e]

Value: 1.60217662E-19 C

Atomic mass unit

Atomic mass unit is a standard unit of mass used to express atomic and molecular weights on a scale relative to the mass of an unbound neutral atom of carbon-12.

Symbol: [Atomic-m]

Value: 1.66054E-27 kg

Other formulas in Distance of Closest Approach category

Go Velocity of alpha particle using distance of closest approach

v = \sqrt{\frac{[Coulomb] \cdot Z \cdot ({[Charge-e]}^{2})}{[Atomic-m] \cdot r 0}}

Go Internal Energy of Ideal Gas using Law of Equipartition Energy

U EP = (\frac{F}{2}) \cdot N moles \cdot [R] \cdot T g

How to Evaluate Distance of closest approach?

Distance of closest approach evaluator uses Distance of Closest Approach = ([Coulomb]*4*Atomic Number*([Charge-e]^2))/([Atomic-m]*(Velocity of alpha particle^2)) to evaluate the Distance of Closest Approach, The Distance of closest approach formula is defined as is the distance to which an alpha particle comes closer to the nucleus. Distance of Closest Approach is denoted by r₀ symbol.

How to evaluate Distance of closest approach using this online evaluator? To use this online evaluator for Distance of closest approach, enter Atomic Number (Z) & Velocity of alpha particle (v) and hit the calculate button.

FAQs on Distance of closest approach

What is the formula to find Distance of closest approach?

The formula of Distance of closest approach is expressed as Distance of Closest Approach = ([Coulomb]*4*Atomic Number*([Charge-e]^2))/([Atomic-m]*(Velocity of alpha particle^2)). Here is an example- 2.4E+19 = ([Coulomb]*4*17*([Charge-e]^2))/([Atomic-m]*(6.34^2)).

How to calculate Distance of closest approach?

With Atomic Number (Z) & Velocity of alpha particle (v) we can find Distance of closest approach using the formula - Distance of Closest Approach = ([Coulomb]*4*Atomic Number*([Charge-e]^2))/([Atomic-m]*(Velocity of alpha particle^2)). This formula also uses Coulomb constant, Charge of electron, Atomic mass unit constant(s).

Can the Distance of closest approach be negative?

Yes, the Distance of closest approach, measured in Length can be negative.

Which unit is used to measure Distance of closest approach?

Distance of closest approach is usually measured using the Angstrom[A] for Length. Meter[A], Millimeter[A], Kilometer[A] are the few other units in which Distance of closest approach can be measured.

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Distance of closest approach Formula

Distance of closest approach Example

Distance of closest approach Solution

Distance of closest approach Formula Elements

Other formulas in Distance of Closest Approach category

How to Evaluate Distance of closest approach?

FAQs on Distance of closest approach

Variable Name