Question

In: Physics

Beginning with the Weizsäcker semi-empirical mass formula, show that the minimum in a mass parabola occurs...

Beginning with the Weizsäcker semi-empirical mass formula, show that the minimum in a mass parabola occurs at a value of atomic number, Zmin, given by

Note: The Weizsäcker semi-empirical mass formula for the binding energy, B, of a nucleus is where A is the atomic mass number of the nucleus and Z is the atomic number of the nucleus. Hint: Although atomic number, Z, only takes integer values, assume it is a continuous variable for the purpose of this exercise.

The expression for atomic mass, m, at the bottom of Page 4/10 of the lecture notes can then be regarded as a quadratic function of Z.

Take ¶m/¶Z, the partial derivative of the expression as a function of Z. ¶m/¶Z is zero at the minimum value of m. Therefore, setting ¶m/¶Z to zero and solving for Z gives you Zmin. Zmin = mn −m p ( −me )c2 +aC A−1/3 +4asym 2aC A−1/3 +8asym A−1 B=+ aV A − aS A2/3 − aC Z(Z −1) A1/3 − asym (A−2Z ) 2 A −aP 1 A3/4

Solutions

Expert Solution

WU (9 we know that wizsachors nomi empirical mass formula are, M4, ) = 2Mp + N Man - B.E. -0 M1A, 2) atomic mass of isolofe Also, ZNA z> murmber of trotomia, N> meignten of neutams. B.E. (Binding energj >-1-20A +08A% A4_, ZZ) , > mas poton moos di matton A So, we can to write aan aro, m/n, 2) - Zm+(A-2) Mm - QUAT A 2 1 @ 2120 + om 1A-22) moso neglecting 's 2 toring 2(2-1) = 2², we got, M(A2) 2mp+ (1-2) Min-03 +09+34.922%va + am 1,72237 Now, to for min'z, (for constant A egn @ toon con lo rodunod an . Red, FAZ ACMm-ag+am) a At $ 2-4am - (Mon-imp) 92 1 / CQ A3 - 4m - MCA,Z) = PA +62 +922 - So, (dm = $ + 2q2 at Z = Knion 1 Zimin = -39,22 m A lan) Bu substituting values of Mary Mp sam, ac we gel Zmin = A/(1.98 +0.015 A2) Are


Related Solutions

Use the Semi Empirical Mass Formula to calculate the kinetic energy of an alpha particle (42He)...
Use the Semi Empirical Mass Formula to calculate the kinetic energy of an alpha particle (42He) emitted in the process 235U → 231Th + α.The bond energy of the α-particle is 28.3 MeV.
what is the empirical formula and the empirical formula mass (g/mol) of a compound composed of...
what is the empirical formula and the empirical formula mass (g/mol) of a compound composed of 31.0% oxygen, 8.06% hydrogen, and 60.1% carbon by mass.
Empirical Formula
A given compound has 52.00% of Chromium and 48.00% of Oxygen . Determine its empirical formula.
Determine the empirical formula for each compound from the molecular formula. molecular formula=C3H6 empirical formula= molecular...
Determine the empirical formula for each compound from the molecular formula. molecular formula=C3H6 empirical formula= molecular formula=C6H12O6 empirical formula=
A compound with the empirical formula of CH4O and a molar mass of 32 g/mol has...
A compound with the empirical formula of CH4O and a molar mass of 32 g/mol has a molecular formula of:
The empirical formula for a compound is CH2Cl and its molar mass is 98.96g/mol. What is...
The empirical formula for a compound is CH2Cl and its molar mass is 98.96g/mol. What is the molecular formula for the compound?
Calculate the empirical formula for each of the following natural flavors based on their elemental mass...
Calculate the empirical formula for each of the following natural flavors based on their elemental mass percent composition. 1.) Nitroglycerin (used medically as a vasodilator to treat heart conditions): 15.87%C, 2.22%H, 18.50%N, and 63.41%O. 2.) Glucose (a source of energy and metabolic intermediate): 40.00%C, 6.71%H, and 53.29%O.
A compound with the empirical formula CH2 has a molar mass of 98 g/mol. What is...
A compound with the empirical formula CH2 has a molar mass of 98 g/mol. What is the molecular formula for this compound? 2-A compound is 54.53% C, 9.15% H, and 36.32% O by mass. What is its empirical formula? 3-The molecular mass of the compound is 132 amu. What is the molecular formula? 4What is the empirical formula of a compound composed of 3.25% hydrogen (H), 19.36% carbon (C), and 77.39% oxygen (O) by mass? 5What is the empirical formula...
Please answer all! 1. What is the empirical formula of C8H6O3? 2. What is the mass...
Please answer all! 1. What is the empirical formula of C8H6O3? 2. What is the mass of 0.0400 moles of potassium carbonate? 3. What is the mass of 0.0500 moles of aluminum sulfate? 4. A sample of calcium that contains twice Avogadro’s number of atoms has a mass of ___?
The empirical formula of styrene is CH; the molar mass of styrene is 104.14 g/mol. How...
The empirical formula of styrene is CH; the molar mass of styrene is 104.14 g/mol. How many H atoms are present in a 4.825g sample of styrene? ___ H atoms (Give your answer in e format. For example 12014 = 1.2014e+05)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT