Distance of closest approach Calculator

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Distance of Closest Approach

Bohr's Atomic Model

Compton Effect

De Broglie Hypothesis

Heisenberg's Uncertainty Principle

Important Formulas on Bohr's Atomic Model

Photo Electric Effect

Planck Quantum Theory

Rutherford Scattering

Schrodinger Wave Equation

Sommerfeld Model

Structure of Atom

✖Atomic Number is the number of protons present inside the nucleus of an atom of an element.ⓘ Atomic Number [Z]			+10% -10%
✖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).ⓘ Velocity of alpha particle [v]			+10% -10%

✖Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus.ⓘ Distance of closest approach [r₀]

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Formula

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Distance of closest approach

Formula

`"r"_{"0"} = ("[Coulomb]"*4*"Z"*("[Charge-e]"^2))/("[Atomic-m]"*("v"^2))`

Example

`"2.4E^9A"=("[Coulomb]"*4*"17"*("[Charge-e]"^2))/("[Atomic-m]"*(("6.34m/s")^2))`

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Distance of closest approach Solution

STEP 0: Pre-Calculation Summary

Formula Used

Distance of Closest Approach = ([Coulomb]*4*Atomic Number*([Charge-e]^2))/([Atomic-m]*(Velocity of alpha particle^2))
r₀ = ([Coulomb]*4*Z*([Charge-e]^2))/([Atomic-m]*(v^2))
This formula uses 3 Constants, 3 Variables

Constants Used

[Charge-e] - Charge of electron Value Taken As 1.60217662E-19
[Atomic-m] - Atomic mass unit Value Taken As 1.66054E-27
[Coulomb] - Coulomb constant Value Taken As 8.9875E+9

Variables Used

Distance of Closest Approach - (Measured in Meter) - Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus.
Atomic Number - Atomic Number is the number of protons present inside the nucleus of an atom of an element.
Velocity of alpha particle - (Measured in Meter per Second) - 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).

STEP 1: Convert Input(s) to Base Unit

Atomic Number: 17 --> No Conversion Required
Velocity of alpha particle: 6.34 Meter per Second --> 6.34 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r₀ = ([Coulomb]*4*Z*([Charge-e]^2))/([Atomic-m]*(v^2)) --> ([Coulomb]*4*17*([Charge-e]^2))/([Atomic-m]*(6.34^2))

Evaluating ... ...

r₀ = 0.23504079171485

STEP 3: Convert Result to Output's Unit

0.23504079171485 Meter -->2350407917.1485 Angstrom (Check conversion here)

FINAL ANSWER

2350407917.1485 ≈ 2.4E+9 Angstrom <-- Distance of Closest Approach

(Calculation completed in 00.004 seconds)

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Created by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

Akshada Kulkarni has created this Calculator and 500+ more calculators!

Verified by Suman Ray Pramanik

Indian Institute of Technology (IIT), Kanpur

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< 3 Distance of Closest Approach Calculators

Velocity of alpha particle using distance of closest approach

Go Velocity of alpha particle = sqrt(([Coulomb]*Atomic Number*([Charge-e]^2))/([Atomic-m]*Distance of Closest Approach))

Distance of closest approach

Go Distance of Closest Approach = ([Coulomb]*4*Atomic Number*([Charge-e]^2))/([Atomic-m]*(Velocity of alpha particle^2))

Internal Energy of Ideal Gas using Law of Equipartition Energy

Go Internal Molar Energy given EP = (Degree of Freedom/2)*Number of Moles*[R]*Temperature of Gas

Distance of closest approach Formula

Distance of Closest Approach = ([Coulomb]*4*Atomic Number*([Charge-e]^2))/([Atomic-m]*(Velocity of alpha particle^2))
r₀ = ([Coulomb]*4*Z*([Charge-e]^2))/([Atomic-m]*(v^2))

What is distance of closest approach?

When an alpha particle is projected towards a nucleus, it retards due to repulsion from the nucleus because both are positively charged. A distance from the nucleus may exist where the alpha particle stops and then rebounds back due to a very strong repulsion from the nucleus. The distance up to which alpha particle comes closer to the nucleus is called the distance of the closest approach. Its value can be determined by the conservation of energy principle.

How to Calculate Distance of closest approach?

Distance of closest approach calculator uses Distance of Closest Approach = ([Coulomb]*4*Atomic Number*([Charge-e]^2))/([Atomic-m]*(Velocity of alpha particle^2)) to calculate 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 calculate Distance of closest approach using this online calculator? To use this online calculator for Distance of closest approach, enter Atomic Number (Z) & Velocity of alpha particle (v) and hit the calculate button. Here is how the Distance of closest approach calculation can be explained with given input values -> 2.4E+19 = ([Coulomb]*4*17*([Charge-e]^2))/([Atomic-m]*(6.34^2)).

FAQ

What is 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 and is represented as r₀ = ([Coulomb]*4*Z*([Charge-e]^2))/([Atomic-m]*(v^2)) or Distance of Closest Approach = ([Coulomb]*4*Atomic Number*([Charge-e]^2))/([Atomic-m]*(Velocity of alpha particle^2)). Atomic Number is the number of protons present inside the nucleus of an atom of an element & 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).

How to calculate 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 is calculated using Distance of Closest Approach = ([Coulomb]*4*Atomic Number*([Charge-e]^2))/([Atomic-m]*(Velocity of alpha particle^2)). To calculate Distance of closest approach, you need Atomic Number (Z) & Velocity of alpha particle (v). With our tool, you need to enter the respective value for Atomic Number & Velocity of alpha particle 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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