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Fundamentals Of Physics
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Short Answer

What is the binding energy per nucleon of the americium isotope Am95244? Here are some atomic masses and the neutron mass.

Am95244 244.064279 u H1 1.007825 un 1.008665 u

The binding energy per nucleon of the americium isotope is 7.52 MeV.

See the step by step solution

Step by Step Solution

Step 1: The given data

The given isotope americium is A95244m.

The atomic mass unit of the isotope americium, MAm=244.064279u

The atomic mass of the hydrogen, MH=1.007825u

The atomic mass unit of neutron, Mn=1.008665u

Step 2: Understanding the concept of binding energy  

The binding energy of an element is defined as the amount of energy required to separate a particle from a system of particles or to disperse all the particles of the system. It can simply also be stated as the product of mass defect with the square of the speed of light. This relation will give the required binding energy of the isotope americium. Now, using this value and dividing it by the number of nucleons of the isotope, we can get the binding energy per nucleon of the americium isotope.

Formulae:

The binding energy of an atom,

Ebe=mc2 =ZMH+A-ZMn-Matomc2 (1)

where, Z is the atomic number (number of protons), A is the mass number (number of nucleons), MH is the mass of a hydrogen atom, Mn is the mass of a neutron, and Matom is the mass of an atom. In principle, nuclear masses should be used, but the mass of the Z electrons included in ZMH is canceled by the mass of the Z electrons included in Matom, so the result is the same.

The binding energy per nucleon of an atom,

EBEper nude on=EbeA (2)

Step 3: Calculation of the binding energy per nucleon of americium

At first, we can calculate the mass excess or the mass defect for the americium isotope by Z = 95 using equation (1) as follows:

m=951.007825 u+244-951.008665 u-244.064279 u =1.970181 u

Now, the binding energy can be calculated by converting the amu value of mass defect into MeV considering equation (1) as follows:

Ebe=(1.970181u)(931.5 Me/u) =1835.212 MeV

Thus, according to the concept the binding energy per nucleon of americium isotope with nucleon number can be calculated using equation (2) as follows:

EBE per nucleon=1835.212MeV/244 =7.52 MeV

Hence, the required value of energy is 7.52 MeV.

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