Question

The binding energy of helium -4 is 28 MeV. a. What is the mass of a helium nucleus (round to 5 decimal places)?

Answer 1

To calculate the mass of a helium-4 nucleus from its binding energy, first convert the binding energy into mass units using E=mc^2, and then subtract the mass defect from the sum of the individual nucleon masses.

Step-by-step explanation:

The mass of a helium nucleus can be found by using the concept of mass defect and binding energy. The mass defect is the difference between the mass of a completely assembled nucleus and the sum of the masses of its nucleons (protons and neutrons). Given that the binding energy (BE) of a helium-4 nucleus is 28 MeV, we can use Einstein's mass-energy equivalence principle E=mc2 to determine the mass defect. The mass defect (in kilograms) is calculated by dividing the binding energy by the square of the speed of light in a vacuum (c2). After obtaining the mass defect in kg, we subtract it from the sum of the masses of two protons and two neutrons to find the mass of the helium nucleus. Please note that 1 MeV = 1.60218×10-13 J, the mass of one nucleon is approximately 1.008665 u for a neutron, and 1.007276 u for a proton, and 1 u = 1.66054×10-27 kg.

Answer 2

4.001805 amu

Step-by-step explanation:

931 Mev = 1 amu

28 Mev = 28 / 931 Mev

= .030075 amu

Helium nucleus consists of 2 proton and 2 neutron .

Binding energy in terms of amu

= total mass of 2 neutron and 2 proton - mass of nucleus of helium

mass of nucleus of helium = total mass of 2 neutron and 2 proton -Binding energy in terms of amu

mass of 2 neutron = 2 x 1.008664 = 2.017328

mass of 2 proton = 2 x 1.007276 = 2.014552

total = 4.03188

So mass of helium nucleus = 4.03188 - .030075

= 4.001805 amu.