Question

Question 3, and 4

2.(50 pts) For the following list of nuclides, complete the following:

List the number of protons

Hydrogen-1= 1

Iron-56 =26

Zirconium-91= 40

Gold-197 =79

Uranium-238: 92

List the number of neutrons

Hydrogen-1 = 0

Iron-56 = 30

Zirconium-91 = 51

Gold-197 = 118

Uranium-238: 146

Write out the nuclide in the form  

Hydrogen-1 = 1 H 1

Iron-56 = 56 Fe 26

Zirconium-91 = 91 Zr 40

Gold-197 = 197 Au 79

Uranium-238 = 238 U 92

Calculate the mass defect of each nuclide and associated binding energy

Hydrogen-1 (mass defect = .007316 amu ) (Total mass = 1.007316)

Iron-56 : (Mass Defect = 0.450166 amu) (Total Mass = 56.450166)

Zirconium-91 (Mass defect = 0.734555 amu) (total mass = 91 amu)

Gold-197(Mass defect = 1.600434 amu) (Total mass = 198.600434)

Uranium-238: (Mass defect= -1.934205) Total mass = 92 x 1.007316 + 146 x 1.008665 = 239.9 0r 238

3. (10 pts) For the isotopes in the previous problem, indicate if they are naturally occurring and/or radioactive. If radioactive, provide the half-life. If naturally occurring, provide the isotopic percentage.

4. (10 pts) For the isotopes in problem 2, calculate the binding energy per nucleon and plot this value versus the mass number.

Answer 1

3.Ans). H¹ is naturally occurring isotope. Isotopic percentage = 99.98 %

Fe⁵⁶  is naturally occurring isotope. Isotopic percentage = 91.754 %

Zr⁹¹ is naturally occurring isotope. Isotopic percentage = 11.22 %

Au¹⁹⁷ is naturally occurring isotope. Isotopic percentage = 100 %

U²³⁸ is a radioactive isotope. Half life = 4.468 billon years

4.Ans).  Binding Energy = binding energy is the energy required to split a nucleus of an atom into its components.The value of binding energy per nucleon gives a measure of the stability of that nucleus. Greater is the binding energy per nucleon of a nucleus, more stable is the nucleus. It is calculated as :

Binding Energy = ( Mass Defect x 931.5 MeV ) / no. of nucleons

According to the mass defects values provided in question, following results are obtained for Binding Energies :

Elements	Binding Energy (MeV)	Mass Number
H1	(0.007316 x 931.5) / 1 = 6.815	1
Fe56	(0.450166 x 931.5) / 56 = 7.488	56
Zr91	(0.734555 x 931.5) / 91 = 7.519	91
Au197	(1.600434 x 931.5) / 197 = 7.568	197
U238	(1.934205 x 931.5) / 238 = 7.570	238

Binding energy per nucleon versus the mass number plot :

Thanks