Question

Given the following information: Mass of proton = 1.00728 amu Mass of neutron = 1.00866 amu Mass of electron = 5.486 × 10^-4 amu Speed of light = 2.9979 × 10^8 m/s Calculate the nuclear binding energy (absolute value) of 3Li^6. which has an atomic mass of 6.015126 amu. J/mol.

Answer 1

Answer: The nuclear binding energy of the given element is $2.938\times 10^{12}J/mol$

Explanation:

For the given element $_3^6\textrm{Li}$

Number of protons = 3

Number of neutrons = (6 - 3) = 3

We are given:

$m_p=1.00728amu\\m_n=1.00866amu\\A=6.015126amu$

M = mass of nucleus = $(n_p\times m_p)+(n_n\times m_n)$

$M=[(3\times 1.00728)+(3\times 1.00866)]=6.04782amu$

Calculating mass defect of the nucleus:

$\Delta m=M-A\\\Delta m=[6.04782-6.015126)]=0.032694amu=0.032694g/mol$

Converting this quantity into kg/mol, we use the conversion factor:

1 kg = 1000 g

So,  $0.032694g/mol=0.032694\times 10^{-3}kg/mol$

To calculate the nuclear binding energy, we use Einstein equation, which is:

$E=\Delta mc^2$

where,

E = Nuclear binding energy = ? J/mol

$\Delta m$ = Mass defect = $0.032694\times 10^{-3}kg/mol$

c = Speed of light = $2.9979\times 10^8m/s$

Putting values in above equation, we get:

$E=0.032694\times 10^{-3}kg/mol\times (2.9979\times 10^8m/s)^2\\\\E=2.938\times 10^{12}J/mol$

Hence, the nuclear binding energy of the given element is $2.938\times 10^{12}J/mol$

Answer 2

The binding energy of the lithium nucleus is 2.94 * 10^14 J/mol.

What is binding energy?

The term binding energy refers to the energy that hold the nucleons in the atom together.

We know that the atomic mass of the Li is 6.015126 amu. Note that there are three protons and three neutrons. Hence;

Mass of protons= 3(1.00728 amu) = 3.02184

Mass of neutrons = 3(1.00866 amu)  = 3.02598

Mass defect = (3.02184 + 3.02598) - 6.015126 amu = 0.032694 amu =  0.032694 g/mol

Now;

E = mc^2 = (0.032694 g/mol * (3 * 10^8)^2) = 2.94 * 10^14 J/mol

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