Total Binding Energy of Nucleus Calculator

✖Volume Constant is a constant value which is equal to 14.1 ± 0.02 MeV.ⓘ Volume Constant [a_v]			+10% -10%
✖Mass Number is the sum of the number of protons and the number of neutrons in an atom.ⓘ Mass Number [A]			+10% -10%
✖Surface Energy Constant is a constant value which equals to 13.0±0.1 MeV.ⓘ Surface Energy Constant [a_s]			+10% -10%
✖Coulomb Energy Constant is a constant quantity which equals to 0.595±0.02 MeV.ⓘ Coulomb Energy Constant [a_c]			+10% -10%
✖Atomic Number is the number of protons in an atom.ⓘ Atomic Number [Z]			+10% -10%
✖Asymmetry Energy Constant is a constant quantity which is equal to 19.0±0.9 MeV.ⓘ Asymmetry Energy Constant [a_a]			+10% -10%
✖Pairing Energy Constant is a constant quantity which is equal to ±135 MeV.ⓘ Pairing Energy Constant [a_P]			+10% -10%

✖Total Binding Energy is the amount of energy required to separate a particle from a system of particles or to disperse all the particles of the system.ⓘ Total Binding Energy of Nucleus [B_tot]

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Formula

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Total Binding Energy of Nucleus

Formula

`"B"_{"tot"} = "a"_{"v"}*"A"-"a"_{"s"}*("A"^(2/3))-"a"_{"c"}*"Z"*("Z"-1)*("A"^(-1/3))-"a"_{"a"}*("A"-2*"Z")^2*("A"^(-1))-"a"_{"P"}*("A"^(-1))`

Example

`"341.8872MeV"="14.1002MeV"*"40"-"13.05MeV"*(("40")^(2/3))-"0.595MeV"*"20"*("20"-1)*(("40")^(-1/3))-"19.2MeV"*("40"-2*"20")^2*(("40")^(-1))-"135MeV"*(("40")^(-1))`

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Total Binding Energy of Nucleus Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Binding Energy = Volume Constant*Mass Number-Surface Energy Constant*(Mass Number^(2/3))-Coulomb Energy Constant*Atomic Number*(Atomic Number-1)*(Mass Number^(-1/3))-Asymmetry Energy Constant*(Mass Number-2*Atomic Number)^2*(Mass Number^(-1))-Pairing Energy Constant*(Mass Number^(-1))
B_tot = a_v*A-a_s*(A^(2/3))-a_c*Z*(Z-1)*(A^(-1/3))-a_a*(A-2*Z)^2*(A^(-1))-a_P*(A^(-1))
This formula uses 8 Variables

Variables Used

Total Binding Energy - (Measured in Megaelectron-Volt) - Total Binding Energy is the amount of energy required to separate a particle from a system of particles or to disperse all the particles of the system.
Volume Constant - (Measured in Megaelectron-Volt) - Volume Constant is a constant value which is equal to 14.1 ± 0.02 MeV.
Mass Number - Mass Number is the sum of the number of protons and the number of neutrons in an atom.
Surface Energy Constant - (Measured in Megaelectron-Volt) - Surface Energy Constant is a constant value which equals to 13.0±0.1 MeV.
Coulomb Energy Constant - (Measured in Megaelectron-Volt) - Coulomb Energy Constant is a constant quantity which equals to 0.595±0.02 MeV.
Atomic Number - Atomic Number is the number of protons in an atom.
Asymmetry Energy Constant - (Measured in Megaelectron-Volt) - Asymmetry Energy Constant is a constant quantity which is equal to 19.0±0.9 MeV.
Pairing Energy Constant - (Measured in Megaelectron-Volt) - Pairing Energy Constant is a constant quantity which is equal to ±135 MeV.

STEP 1: Convert Input(s) to Base Unit

Volume Constant: 14.1002 Megaelectron-Volt --> 14.1002 Megaelectron-Volt No Conversion Required
Mass Number: 40 --> No Conversion Required
Surface Energy Constant: 13.05 Megaelectron-Volt --> 13.05 Megaelectron-Volt No Conversion Required
Coulomb Energy Constant: 0.595 Megaelectron-Volt --> 0.595 Megaelectron-Volt No Conversion Required
Atomic Number: 20 --> No Conversion Required
Asymmetry Energy Constant: 19.2 Megaelectron-Volt --> 19.2 Megaelectron-Volt No Conversion Required
Pairing Energy Constant: 135 Megaelectron-Volt --> 135 Megaelectron-Volt No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

B_tot = a_v*A-a_s*(A^(2/3))-a_c*Z*(Z-1)*(A^(-1/3))-a_a*(A-2*Z)^2*(A^(-1))-a_P*(A^(-1)) --> 14.1002*40-13.05*(40^(2/3))-0.595*20*(20-1)*(40^(-1/3))-19.2*(40-2*20)^2*(40^(-1))-135*(40^(-1))

Evaluating ... ...

B_tot = 341.887233004295

STEP 3: Convert Result to Output's Unit

5.47763974135912E-11 Joule -->341.887233004295 Megaelectron-Volt (Check conversion here)

FINAL ANSWER

341.887233004295 ≈ 341.8872 Megaelectron-Volt <-- Total Binding Energy

(Calculation completed in 00.004 seconds)

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Go Unknown Amount of Active Compound = Amount of Inactive Isotope of Same Compound*(Specific Activity of Mixed Compound/(Specific Activity of Pure Labelled Compound-Specific Activity of Mixed Compound))

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Age of Minerals and Rocks containing Pure Thorium and Pb-208

Go Age of Mineral and Rocks for Pure Th/Pb-208 system = 46.2*(10^9)*log10(1+(1.116*Number of Pb-208 present in Mineral/Rock Sample)/Number of Th-232 present in Mineral/Rock Sample)

Age of Minerals and Rocks containing Pure Uranium and Pb-206

Go Age of Mineral and Rocks for Pure U/Pb-206 system = 15.15*(10^9)*log10(1+(1.158*Number of Pb-206 present in Mineral/Rock Sample)/Number of U-238 present in Mineral/Rock Sample)

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Total Binding Energy of Nucleus Formula

What is the Liquid-Drop Model Analogy?

A model of the atomic nucleus that has been successful in accounting for nuclear fission and the variation of nuclear stability with mass number. The density of a nucleus is independent of its size, which suggests that nuclear matter can be modelled on a drop of an incompressible liquid, such as water. Different excitation states of a drop-like nucleus can then be described in terms of spherical harmonics. The success of the model has been associated with the fact that the binding forces in both the nucleus and the liquid drop are essentially short-ranged. The liquid-drop model provides a subtle explanation for the variation of binding energy in different nuclei.

How to Calculate Total Binding Energy of Nucleus?

Total Binding Energy of Nucleus calculator uses Total Binding Energy = Volume Constant*Mass Number-Surface Energy Constant*(Mass Number^(2/3))-Coulomb Energy Constant*Atomic Number*(Atomic Number-1)*(Mass Number^(-1/3))-Asymmetry Energy Constant*(Mass Number-2*Atomic Number)^2*(Mass Number^(-1))-Pairing Energy Constant*(Mass Number^(-1)) to calculate the Total Binding Energy, The Total Binding Energy of Nucleus formula is given by combining all the energy terms that are present and working on the nucleus of an element. Total Binding Energy is denoted by B_tot symbol.

How to calculate Total Binding Energy of Nucleus using this online calculator? To use this online calculator for Total Binding Energy of Nucleus, enter Volume Constant (a_v), Mass Number (A), Surface Energy Constant (a_s), Coulomb Energy Constant (a_c), Atomic Number (Z), Asymmetry Energy Constant (a_a) & Pairing Energy Constant (a_P) and hit the calculate button. Here is how the Total Binding Energy of Nucleus calculation can be explained with given input values -> 2.1E+15 = 2.25910207884661E-12*40-2.09084141565001E-12*(40^(2/3))-9.53295511350004E-14*20*(20-1)*(40^(-1/3))-3.07618047360001E-12*(40-2*20)^2*(40^(-1))-2.16293939550001E-11*(40^(-1)).

FAQ

What is Total Binding Energy of Nucleus?

The Total Binding Energy of Nucleus formula is given by combining all the energy terms that are present and working on the nucleus of an element and is represented as B_tot = a_v*A-a_s*(A^(2/3))-a_c*Z*(Z-1)*(A^(-1/3))-a_a*(A-2*Z)^2*(A^(-1))-a_P*(A^(-1)) or Total Binding Energy = Volume Constant*Mass Number-Surface Energy Constant*(Mass Number^(2/3))-Coulomb Energy Constant*Atomic Number*(Atomic Number-1)*(Mass Number^(-1/3))-Asymmetry Energy Constant*(Mass Number-2*Atomic Number)^2*(Mass Number^(-1))-Pairing Energy Constant*(Mass Number^(-1)). Volume Constant is a constant value which is equal to 14.1 ± 0.02 MeV, Mass Number is the sum of the number of protons and the number of neutrons in an atom, Surface Energy Constant is a constant value which equals to 13.0±0.1 MeV, Coulomb Energy Constant is a constant quantity which equals to 0.595±0.02 MeV, Atomic Number is the number of protons in an atom, Asymmetry Energy Constant is a constant quantity which is equal to 19.0±0.9 MeV & Pairing Energy Constant is a constant quantity which is equal to ±135 MeV.

How to calculate Total Binding Energy of Nucleus?

The Total Binding Energy of Nucleus formula is given by combining all the energy terms that are present and working on the nucleus of an element is calculated using Total Binding Energy = Volume Constant*Mass Number-Surface Energy Constant*(Mass Number^(2/3))-Coulomb Energy Constant*Atomic Number*(Atomic Number-1)*(Mass Number^(-1/3))-Asymmetry Energy Constant*(Mass Number-2*Atomic Number)^2*(Mass Number^(-1))-Pairing Energy Constant*(Mass Number^(-1)). To calculate Total Binding Energy of Nucleus, you need Volume Constant (a_v), Mass Number (A), Surface Energy Constant (a_s), Coulomb Energy Constant (a_c), Atomic Number (Z), Asymmetry Energy Constant (a_a) & Pairing Energy Constant (a_P). With our tool, you need to enter the respective value for Volume Constant, Mass Number, Surface Energy Constant, Coulomb Energy Constant, Atomic Number, Asymmetry Energy Constant & Pairing Energy Constant 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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