Question

Bayron has a rest mass of 1115.7 Mev/c^2. Express this in unified atomic mass units. (ii) From the aproximate radius of the 271Ds nucleus, estimate the volume of the darmstadium-271 nucleus. (b) Calculate the dinding energy per nucleon of plutonium-239, miven Mn 1.0086649 u, m (hydrogen-1 atom)=1.0078250 u, and m (plutonium-239 atom) =239.052157 u.

Answer 1

The rest mass of the baryon in units of atomic mass units is calculated as follows:

  

Therefore, the rest mass of the Baryon in amu is 1.197746 u.

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The radius of the nucleus of an atom is given as follows:

      

       

Therefore, the radius of darmstadium is .

The volume of the nucleus is,

     

          

  

Therefore, the volume of the darmstadium is .

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The total binding energy of a nucleus is,

Here, Z is the atomic number, is the mass of hydrogen atom, N is the number of neutrons, is the mass

of neutron, is the atomic mass, and is the speed of light.

For Plutonium, and .

Then,

     

The binding energy per nucleon is,

  

Here, is the atomic mass number.

Then,

  

Therefore, the binding energy of the nucleon is .