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.
Physics to Elena - Elena, Wednesday, May 8, 2013 at 3:16pm
I believe that the correct answer is 1.58•10¹⁴ J.
Physics to Elena - Leila, Wednesday, May 8, 2013 at 3:49pm
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
Thanks Elena :) I really appreciate your help!
I apologize for any confusion. Let's go through the calculation again to determine the correct answer.
Number of atoms = N(A) * m / μ
= 6.022 * 10^23 * 0.003 / 63.5 * 10^-3
= 2.85 * 10^22
Number of nucleons = 2.85 * 10^22 * 63
= 1.8 * 10^24
Energy = 1.8 * 10^24 * 550 * 10^6 * 1.6 * 10^-19
= 1.8 * 550 * 1.6 * 10^5
= 1.584 * 10^9 J
Therefore, the correct estimate for the energy needed to break a 3.0g copper penny into its constituent nucleons is 1.584 * 10^9 J.
To estimate the energy needed to break a 3.0g copper penny into its constituent nucleons, we need to calculate the number of nucleons in the penny and then multiply it by the binding energy.
First, let's calculate the number of atoms in a 3.0g copper penny. We can use the molar mass of copper to convert the mass into moles.
Molar mass of copper (Cu) = 63.5 g/mol
Number of moles of copper in the penny = mass of copper / molar mass of copper
= 3.0g / 63.5 g/mol
= 0.0472 mol
Now, let's calculate the number of atoms in the penny. Avogadro's number (N_A) gives us the number of atoms in 1 mole of a substance.
Number of atoms in the penny = Number of moles of copper * Avogadro's number
= 0.0472 mol * (6.022 x 10^23 atoms/mol)
≈ 2.84 x 10^22 atoms
Next, we can calculate the total number of nucleons (protons + neutrons) in the penny by multiplying the number of atoms by the average number of nucleons per atom for copper.
Average number of nucleons per atom for copper = 63
Number of nucleons in the penny = Number of atoms * Average number of nucleons per atom
= 2.84 x 10^22 atoms * 63
≈ 1.79 x 10^24 nucleons
Finally, we can calculate the energy needed to break the penny into its constituent nucleons by multiplying the number of nucleons by the binding energy.
Binding energy = 550 MeV = 550 x 10^6 eV = 550 x 10^6 x 1.6 x 10^-19 J
Energy = Number of nucleons * Binding energy
= 1.79 x 10^24 nucleons * (550 x 10^6 x 1.6 x 10^-19 J)
≈ 1.81 x 10^5 J
Therefore, the energy needed to break a 3.0g copper penny into its constituent nucleons is approximately 1.81 x 10^5 Joules.