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skelet666 [1.2K]
3 years ago
10

For each of the following nuclei, determine the binding energy per nucleon (in MeV). (For all masses, keep six places beyond the

decimal point when performing your calculations. Then round your final answer to at least three significant figures.)(a) 21 MeV (b) 4He MeV (c) 180 MeV (d) 23Na MeV
Chemistry
1 answer:
garik1379 [7]3 years ago
3 0

Answer: (a) BE = 1.112 MeV

               (b) BE = 7.074 MeV

               (c) BE = 7.767 MeV

               (d) BE = 8.112 MeV

Explanation: Binding energy per nucleon is the average energy necessary to remove a proton or a neutron from the nucleus of an atom. It is mathematically defined as:

BE = \frac{\Delta m.c^{2}}{A}

Where

Δm is a difference in mass known as <u><em>mass</em></u><em> </em><u><em>defect</em></u>

A is atomic mass of an atom.

Mass Defect is determined by:

\Delta m =Zm_{p}+(A-Z)m_{n} - m_{nuc}

where:

Z is atomic number

m_{p} is mass of proton

m_{n} is mass of neutron

m_{nuc} is mass of the nucleus

Mass of proton is 1.007825u.

Mass of neutron is 1.008665u.

The unit u is equal to 931.5MeV/c².

(a) 2H(deuterion): Given: Z = 1; A = 2; m_{nuc} = 2.014102u

\Delta m =1(1.007825)+1(1.008665) -2.014102

\Delta m =0.002388u

BE = \frac{0.002388.c^{2}}{2}.931.5\frac{MeV}{c^{2}}

BE = 1.112MeV

(b) 4He (Helium): Given: Z = 2; A = 4; m_{nuc} = 4.002603

\Delta m =2(1.007825)+2(1.008665) -4.002603

\Delta m =0.030377u

BE = \frac{0.030377.c^{2}}{4}.931.5\frac{MeV}{c^{2}}

BE = 7.074MeV

(c) 18O (Oxygen): Given: Z = 8; A = 18; m_{nuc} = 17.999160

\Delta m =8(1.007825)+10(1.008665) -17.999160

\Delta m =0.15009u

BE = \frac{0.15009.c^{2}}{18}.931.5\frac{MeV}{c^{2}}

BE = 7.767MeV

(d) 23Na (Sodium): Given: Z = 11; A = 23; m_{nuc} = 22.989767

\Delta m =11(1.007825)+12(1.008665) -22.989767

\Delta m =0.200288u

BE = \frac{0.200288.c^{2}}{23}.931.5\frac{MeV}{c^{2}}

BE = 8.112MeV

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