Nucleus specific charge

The specific charge of a nucleus can be found by adding the charges and masses of the particles together, then doing charge\div mass as usual.

• The charge can be found by multiplying the number of protons by the charge of the proton.
  • We ignore the neutrons because they have no charge.
• The mass is found by taking the nucleon number (mass number), or adding the number of protons and neutrons, then multiplying by the mass of a proton/neutron, 1.67\times10^{-27}

Examples

Specific charge of ^1_1H nucleus

• 1 proton
• No neutrons
• No electrons as nucleus
• \text{specific charge} = \frac{1.6\times10^{-19}}{1.67\times10^{-27}}\times\frac{1}{1}
• \text{specific charge}=9.58\times10^{7}

Specific charge of ^7_3Li nucleus

• 3 protons
• 7 sum of protons and neutrons
• No electrons as nucleus
• \text{specific charge} = \frac{1.6\times10^{-19}}{1.67\times10^{-27}}\times\frac{4}{7}
• \text{specific charge}=4.11\times10^{7}

Specific charge of ^{12}_6C nucleus

• 6 protons
• 12 sum of protons and neutrons
• No electrons as nucleus
• \text{specific charge} = \frac{1.6\times10^{-19}}{1.67\times10^{-27}}\times\frac{6}{12}
• \text{specific charge}=4.79\times10^{7}

Specific charge of ^{197}_{79}Au nucleus

• 79 protons
• 197 sum of protons and neutrons
• No electrons as nucleus
• \text{specific charge} = \frac{1.6\times10^{-19}}{1.67\times10^{-27}}\times\frac{79}{197}
• \text{specific charge}=3.84\times10^{7}

Specific charge of ^{238}_{92}U nucleus

• 92 protons
• 238 sum of protons and neutrons
• No electrons as nucleus
• \text{specific charge} = \frac{1.6\times10^{-19}}{1.67\times10^{-27}}\times\frac{92}{238}
• \text{specific charge}=3.70\times10^{7}

A nucleus has 92 protons and 143 neutrons: find the specific charge

• Relative charge = 92
• Relative mass = 92+143=235
• Charge = 92\times1.6\times10^{-19}=1.472\times10^{-17}
• Mass = 235\times1.67\times10^{-27}=3.9245\times10^{-25}
• specific charge = \frac{1.472\times10^{-17}}{3.9245\times10^{-25}}
• specific charge = 1.48\times10^7

The specific charge is 3.7\times10^7 of a uranium nucleus: find the number of neutrons

• 92 protons
• Relative charge = 92
• Charge = 1.472\times10^{-17}
• \text{mass}=\text{charge}\div\text{specific charge}
• \text{mass}=\frac{1.472\times10^{-17}}{3.7\times10^7}
• Mass = 3.978\times10^{-25}
• Relative mass = \frac{3.978\times10^{-25}}{1.67\times10^{-27}}\approx238
• Number of neutrons = relative mass - number of protons
• Number of neutrons = 238-92=146

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