How to Calculate the Energy of Helium

Each helium atom in these balloons has nuclear binding energy

Albert Einstein's 1905 discovery of the relationship between mass and energy led to nuclear-based technology, including nuclear power plants and nuclear weapons. It also brought an understanding of the energy generation mechanism of stars. Central to this field is the calculation of the nuclear binding energy of a nucleus, more specifically in this case the helium nucleus, which has the chemical symbol He. The nuclear binding energy is the the energy that holds the helium nucleus together and is the amount of energy liberated when the nucleus breaks into its constituent parts. These parts are the two protons and two neutrons inside the helium nucleus.

Instructions

1. Multiply the number of protons by the mass of a proton in atomic mass units ("u") and call this quantity A. The mass of a proton is 1.007825u, so A = 2.015650 u.

2. Multiply the number of neutrons by the mass of a neutron in atomic mass units and call this quantity B. The mass of a neutron is 1.008665 u, so B = 2.017330 u.

3. Calculate the mass difference between the sum of the particles that make up the nucleus and the nucleus mass. To do this, add together A and B. Then subtract the mass of the helium nucleus which is 4.0015058 u.

   A + B - He nucleus mass

   = 2.015650 u + 2.0173300 u - 4.001506 u

   = 0.031474 u

   = 0.030377 u.

4. Utilize Einstein's famous equation E = m c^2, where E is the nuclear binding energy, m is the mass difference in, and c is the speed of light in units of "MeV / u". Note that c^2 = 931.50 MeV / u.

   E = m c^2

   = (0.031474 u) x ( 931.50 MeV /u)

   = 29.32 MeV.

   The nuclear binding energy of helium is 29.32 MeV.

Tips & Warnings

• Keep at least six decimal places for masses to make accurate calculations of nuclear binding energy.

• Conversion from MeV to joules is accomplished by multiplying by 1.602 x 10^ -12.

• The masses of atomic nuclei can be determined by first finding the atom's mass on a periodic table and subtracting the total mass of all the electrons the atom contains. The mass of an electron is 5.485799 x 10^ -4 u.

References

• "Physics for Scientists and Engineers"; Raymond A. Serway; 1992

Resources

• HyperPhysics at Georgia State University: Nuclear Binding Energy
• Carnegie Mellon University: Online Periodic Table
• HyperPhysics at Georgia State University: Nuclear Units