Estimate the total binding energy for copper.
550 MeV
Estimate the energy, in joules, needed to break a 3.0g copper penny into its constituent nucleons.
E= in Joules
Please help me out I got 1st part I need the Energy in joules am confused please help me out...thanks
Physics - Elena, Wednesday, May 8, 2013 at 6:33am
Number of atoms is
N= N(A)•m/μ =
=6.022•10²³•0.003/63.5•10⁻³=2.85•10²².
Number of nucleons (protons+neutrons) =
=2.85•10²²•63=1.8•10²⁴.
Energy = 1.8•10²⁴•550•10⁶•1.6•10⁻¹⁹ =1.58•10⁸ J
Thanks for the help but 1.58x10^8 J is wrong n I recalculated you calculation I got 1.58x10^14 J but that was also wrong so could you plz help me out.
I believe that the correct answer is 1.58•10¹⁴ J.
Thatz what I got too but itz still wrong :/ I don't know why please help me...thanks
Number of nuclei
N=n•N(A) = (m/μ) • N(A)=
=(3 g)•(6.022•10²³ nuclei/mol)/(63 g/mol)=2.87•10²² nuclei
The energy required to break all the copper nuclei into their constituent protons and
neutrons is
(550 MeV ) •(2.87•10²² nuclei) =1.56•10²⁵ MeV =
=1.56•10³¹eV =2.5•10¹² J
To estimate the energy needed to break a 3.0g copper penny into its constituent nucleons, we need to consider the number of atoms in the penny and the binding energy per nucleon.
First, let's determine the number of atoms in the penny. Given that the atomic mass of copper (Cu) is approximately 63.5 grams/mole and the mass of the penny is 3.0 grams, we can use Avogadro's number (6.022 x 10^23 atoms/mole) to calculate the number of atoms:
Number of atoms = (Number of moles of Cu) * Avogadro's number
= (3.0 g / 63.5 g/mole) * (6.022 x 10^23 atoms/mole)
≈ 2.84 x 10^22 atoms
Next, we need to determine the total number of nucleons (protons + neutrons) in the penny. Since copper has an atomic number of 29 and the number of nucleons is equal to the atomic number multiplied by the number of atoms, we can calculate:
Number of nucleons = Atomic number * Number of atoms
= 29 * 2.84 x 10^22
≈ 8.24 x 10^23 nucleons
Now, we can calculate the total energy needed to break the penny by multiplying the number of nucleons by the binding energy per nucleon. In this case, the given binding energy for copper is 550 MeV:
Energy = Number of nucleons * Binding energy per nucleon
= 8.24 x 10^23 nucleons * 550 MeV/nucleon
To convert MeV to Joules, we can use the conversion factor 1 MeV = 1.6 x 10^-13 Joules:
Energy = (8.24 x 10^23) * (550 x 1.6 x 10^-13) Joules
≈ 7.1 x 10^11 Joules
Therefore, the estimated energy needed to break a 3.0g copper penny into its constituent nucleons is approximately 7.1 x 10^11 Joules.