Question
The mass of a specific atomic isotope is 165.98546 u. Its binding energy is 1293.155 MeV. Find the atomic number of the isotope. Assume that the nucleon number is approximately equal to the mass of the isotope. Nuclear Properties IDENTIFY the relevant concepts: The key properties of any nucleus include the mass, radius, binding energy, mass defect, binding energy per nucleon, and angular momentum. SET UP the problem using the following steps: Once you have identified your target variables, collect the equations you need to solve the problem. Make sure that you understand the meaning of each equation. EXECUTE the solution as follows: Solve the equations for the target variables. When doing energy calculations involving the binding energy and binding energy per nucleon, note that mass tables almost always list the masses of neutral atoms, including their full complement of electrons. To compensate for this, use the mass MH of a atom in rather than the mass of a bare proton. The binding energies of the electrons in the neutral atoms are much smaller and tend to cancel in the subtraction in the above equation, so don't worry about them. EVALUATE your answer: Familiarity with some typical numerical magnitudes is very useful when checking your results. Protons and neutrons are about 1840 times as massive as electrons. The radius of a nucleus is of the order 10-15 m; the electric potential energy of two protons in a nucleus is of the order 10-13 J or 1 MeV. Thus typical nuclear interaction energies are of the order of a few MeV, rather than a few eV as with atoms. The typical binding energy per nucleon is about 1 % of the rest energy of a nucleon. For comparison, the ionization energy of the hydrogen atom is only 0.003% of the electron's rest energy. What is the atomic number of this isotope? Recall that c2 = 931.5 MeV/u, MH = 1.007825 u, and mn =1.008665 u. Express the atomic number numerically.
Explanation / Answer
Part A
What is the target variable in this question?
Answer: No. of Protons
Part B)
The following equation relates the binding energy of an atom to its atomic number. Identify the variables in this equation.
EB=(ZMH+Nmn?AZM)c2
Answer:
AMZ - Atomic Mass
Z - Atomic Number
Eb - Binding Energy
Mh - mass of a h atom
mn - mass of a neutron
N - no. of neutrons
Part C)
What is the atomic number of this isotope? Recall that c2=931.5 MeV/u, MH=1.007825 u, and mn=1.008665 u.
Answer: Z = 77
Part D)
What is the binding energy per nucleon in iridium-166?
Answer - ?
