Mass Defect Calculator

Understanding the mass defect of a nucleus is essential in nuclear physics. Mass defect refers to the tiny difference between the sum of the masses of protons and neutrons and the actual mass of the nucleus. This small difference in mass is converted into binding energy, which holds the nucleus together.

Our Mass Defect Calculator has been developed to help students, researchers, and physics enthusiasts easily calculate the mass defect of any nucleus. With this tool, you can find the binding energy, binding energy per nucleon, and even convert mass defect into kilograms or energy units like MeV and Joules.

Mass Defect Formula

The mass defect (Δm) can be calculated using the formula:

For nuclear mass:

Δm = (Z × mp + N × mn) − M_nucleus

For atomic mass:

Δm = (Z × (mp + me) + N × mn) − M_atom

Where:

• Δm = mass defect
• Z = number of protons
• N = number of neutrons (A − Z)
• mp = mass of proton
• mn = mass of neutron
• me = mass of electron
• M_nucleus = measured mass of nucleus
• M_atom = measured atomic mass

Once you have the mass defect, you can convert it to binding energy using Einstein’s formula:

E_binding = Δm × c²

Or in units convenient for nuclear physics:

E_binding (MeV) = Δm × 931.494

How to Use Our Online Mass Defect Calculator

1. Enter the number of protons (Z): This is the atomic number of the element.
2. Enter the mass number (A): Total number of protons and neutrons.
3. Provide measured mass: Input the experimental mass of the nucleus or atom.
4. Select mass type: Choose between nuclear mass or atomic mass.
5. Select units for mass and energy: You can enter mass in amu, kg, or MeV, and get energy in MeV or Joules.
6. Click Calculate: The calculator will display mass defect, total binding energy, and binding energy per nucleon.
7. Review step-by-step results: Our tool shows every calculation step for better understanding.

Example Mass Defect Calculation

Let’s calculate the mass defect of Helium-4:

Number of protons (Z) = 2

Mass number (A) = 4

Measured atomic mass = 4.002603 amu

Mass type = Atomic

Step 1 – Number of neutrons:

N = A − Z = 4 − 2 = 2

Step 2 – Total mass of separated particles:

M_separated = Z × (mp + me) + N × mn

= 2 × (1.007276 + 0.0005486) + 2 × 1.008665

= 4.0318766 amu

Step 3 – Mass defect:

Δm = M_separated − M_atom

= 4.0318766 − 4.002603

= 0.0292736 amu

Step 4 – Binding energy in MeV:

E_binding = Δm × 931.494

= 0.0292736 × 931.494

≈ 27.27 MeV

Step 5 – Binding energy per nucleon:

E_per_nucleon = 27.27 / 4 ≈ 6.82 MeV/nucleon

This calculation shows that Helium-4 has a strong nuclear binding energy, making it stable.

How to Convert Mass Defect into Kilograms

If you want the mass defect in kilograms:

Δm_kg = Δm × 1.66053906660 × 10⁻²⁷

Using our example:

Δm_kg = 0.0292736 × 1.66053906660 × 10⁻²⁷ ≈ 4.86 × 10⁻²⁹ kg

This allows you to calculate the exact energy using E = mc² in Joules.

Final Verdict

Our Mass Defect Calculator simplifies the complex calculations of nuclear physics into easy, step-by-step results. Whether you are calculating mass defect, binding energy, or converting units, this tool ensures accurate results without manual errors. It is perfect for students, educators, and anyone interested in understanding nuclear stability.

With our calculator, you can quickly learn the mass defect formula, see detailed calculations, and convert mass into energy easily.

FAQs

What is mass defect in simple terms?

Mass defect is the small difference between the sum of the masses of protons and neutrons and the actual mass of the nucleus. It represents the energy binding the nucleus.

How do you calculate mass defect?

Use Δm = (Z × mp + N × mn) − M_nucleus for nuclear mass, or include electron mass for atomic mass.

How to convert mass defect into kg?

Multiply the mass defect in amu by 1.66053906660 × 10⁻²⁷ to get kilograms.

Can I calculate binding energy from mass defect?

Yes, using E = Δm × c² or E (MeV) = Δm × 931.494.

What is the binding energy per nucleon?

It is the binding energy divided by the total number of nucleons, showing the average energy that holds each nucleon in the nucleus.