Calculate the binding energy per nucleon (in J) for 6Li and 7Li. The atomic masses are 6.015122 u for 6Li, and 7.016004 u for 7Li. (Enter unrounded values. Assume that the mass of 11H = 1.007825 u, mp = 1.007275 u, mn = 1.008666 u, and me = 0.000549 u, respectively.)
Li has 3p, 3e, and 3n. Sum those masses and subtract 6.015122 u . That difference gives you the loss in mass. Then dE = delta m*c^2. For delta m, convert u difference into kg. Post your work if you get stuck.
Well, let me whip out my clown calculator and crunch some numbers for you!
To calculate the binding energy per nucleon, we'll need to find the total binding energy of each nucleus and then divide it by the number of nucleons.
For 6Li:
Atomic mass = 6.015122 u
Number of nucleons = 6 (3 protons + 3 neutrons)
First, let's find the mass difference between the 6Li nucleus and the sum of the individual masses of its constituent particles:
Mass difference = Atomic mass - (3 * mp + 3 * mn)
= 6.015122 u - (3 * 1.007275 u + 3 * 1.008666 u)
Now, let's convert this mass difference to energy using Einstein's equation, E = mc^2:
Binding energy of 6Li = [Mass difference * c^2] J
= [Mass difference * (3 x 10^8 m/s)^2] J
For 7Li:
Atomic mass = 7.016004 u
Number of nucleons = 7 (3 protons + 4 neutrons)
Repeat the same steps as above to find the binding energy of 7Li.
Finally, to find the binding energy per nucleon, divide the binding energy by the number of nucleons for each nucleus.
Don't worry, even though this process seems complex, I'll make sure we don't get too serious! Let's have some fun with numbers! 😉
To calculate the binding energy per nucleon for 6Li and 7Li, we need to determine the total binding energy and the number of nucleons in each nucleus first.
Let's start with 6Li:
The atomic mass of 6Li is 6.015122 u.
The mass of 1 neutron (mn) is 1.008666 u.
The mass of 1 proton (mp) is 1.007275 u.
The mass of 1 electron (me) is 0.000549 u.
To calculate the total binding energy for 6Li, we will subtract the sum of the masses of 3 protons, 3 neutrons, and 3 electrons from the atomic mass of 6Li:
Total mass of 6Li = (3 * mp) + (3 * mn) + (3 * me)
= (3 * 1.007275 u) + (3 * 1.008666 u) + (3 * 0.000549 u)
= 3.021825 u + 3.025998 u + 0.001647 u
= 6.04947 u
Now, we can calculate the total binding energy (E) for 6Li using the formula E = Δmc^2, where Δm is the difference in mass and c is the speed of light:
Δm = (Mass of 6Li - Total mass of 6Li) * (1.66053906660 * 10^-27 kg/u) (to convert unit to kg)
= (6.015122 u - 6.04947 u) * (1.66053906660 * 10^-27 kg/u)
= -0.034348 u * (1.66053906660 * 10^-27 kg/u)
= -5.695672833 * 10^-29 kg
The speed of light (c) is approximately 2.998 * 10^8 m/s.
Using the formula E = Δmc^2, we can calculate the total binding energy:
Total binding energy of 6Li = (-5.695672833 * 10^-29 kg) * (2.998 * 10^8 m/s)^2
= -5.695672833 * 10^-29 kg * (2.998 * 10^8 m/s)^2
= -5.695672833 * 10^-29 kg * 8.988004 * 10^16 m^2/s^2
= -5.11854107606 * 10^-12 J
The number of nucleons in 6Li is 6 (3 protons + 3 neutrons in the nucleus).
Now, we can calculate the binding energy per nucleon (BE/A) for 6Li:
BE/A for 6Li = Total binding energy of 6Li / Number of nucleons in 6Li
= (-5.11854107606 * 10^-12 J) / 6
= -8.53090179343 * 10^-13 J
For 7Li, the calculation is similar.
The atomic mass of 7Li is 7.016004 u.
The total mass of 7Li will be the sum of the masses of 3 protons, 4 neutrons, and 3 electrons:
Total mass of 7Li = (3 * mp) + (4 * mn) + (3 * me)
= (3 * 1.007275 u) + (4 * 1.008666 u) + (3 * 0.000549 u)
= 3.021825 u + 4.034664 u + 0.001647 u
= 7.058136 u
Using the same method as before, we find the total binding energy for 7Li to be -7.64127596 * 10^-13 J.
The number of nucleons in 7Li is 7 (3 protons + 4 neutrons in the nucleus).
Now we can calculate the binding energy per nucleon (BE/A) for 7Li:
BE/A for 7Li = Total binding energy of 7Li / Number of nucleons in 7Li
= (-7.64127596 * 10^-13 J) / 7
= -1.09161085143 * 10^-13 J
Therefore, the binding energy per nucleon for 6Li is approximately -8.53090179343 * 10^-13 J, and for 7Li is approximately -1.09161085143 * 10^-13 J.
To calculate the binding energy per nucleon, we need to determine the binding energy (BE) and the number of nucleons (N) for each isotope.
First, let's find the binding energy (BE) for each isotope using the formula:
BE = Δmc^2
Where Δm is the difference in mass between the isotope and the sum of the masses of its individual nucleons, and c is the speed of light.
For 6Li:
Δm = (6.015122 u - (5 * 1.007275 u) - 0.000549 u)
= 0.092173 u
BE_6Li = Δm * c^2
To use the correct units, we need to convert atomic mass units (u) to kilograms (kg) and multiply by the speed of light squared (c^2) to convert to joules (J):
BE_6Li = (0.092173 kg) * (299,792,458 m/s)^2
≈ 8.71664e-11 J
For 7Li:
Δm = (7.016004 u - (6 * 1.007275 u) - 0.000549 u)
= 0.044681 u
BE_7Li = Δm * c^2
BE_7Li = (0.044681 kg) * (299,792,458 m/s)^2
≈ 4.20753e-11 J
Next, we need to determine the number of nucleons (N) for each isotope.
For 6Li, N = 6
For 7Li, N = 7
Finally, we can calculate the binding energy per nucleon (BEN) using the formula:
BEN = BE / N
For 6Li:
BEN_6Li = BE_6Li / N
= 8.71664e-11 J / 6
For 7Li:
BEN_7Li = BE_7Li / N
= 4.20753e-11 J / 7
Therefore, the binding energy per nucleon for 6Li is approximately BEN_6Li = 1.45277e-11 J, and for 7Li is approximately BEN_7Li = 6.0108e-12 J.