Specific charge

Specific charge compares charge to mass. It is calculated by dividing the charge in coulombs by the mass in kg.

Specific charge equation:

$\text{specific charge = }\frac{\text{charge}}{\text{mass}}$

Where:

• Specific charge is measured in coulombs per kilogram (C kg^-1)
• Charge is measured in Coulombs (C)
• Mass is measured in kilograms (kg)

Worked example 1 - Specific charge of a gold nucleus

Calculate the specific charge of a gold nucleus. Gold has an atomic number of 79. The mass number of gold is 196.96657.

Step 1: Formula

$\text{specific charge = }\frac{\text{charge}}{\text{mass}}$

Step 2: Calculate charge

charge = atomic number x charge of proton

charge = 79 x 1.6 x 10^-19 = 1.264 x 10^-17 C

Step 3: Calculate mass

mass = mass number x atomic mass unit

mass = 196.96657 x 1.67 x 10^-27 = 3.289 x 10^-25 kg

Step 4: Substitution and correct evaluation:

$\text{specific charge = }\frac{\text{charge}}{\text{mass}}$

$\text{specific charge = }\frac{1.264\times {10}^{-17}}{3.289\times {10}^{-25}}=3.84\times {10}^7{\text{ C kg}}^{-1}$

Worked example 2 - Specific charge of magnesium ion (Mg2+)

Calculate the specific charge of a magnesium ion (Mg²⁺). The mass number of Mg is 24.305.

Step 1: Formula

$\text{Specific charge = }\frac{charge}{mass}$

Step 2: Calculate charge

charge = relative charge x elementary charge

charge = 2 x 1.6 x 10^-19 = 3.2 x 10^-19 C

Step 3: Calculate mass

Mass = mass number x atomic mass unit

Mass = 24.305 x 1.67 x 10^-27 = 4.059 x 10^-26 kg

Step 4: Substitution and correct evaluation:

$\text{Specific charge = }\frac{\text{charge}}{\text{mass}}$

$\text{Specific charge = }\frac{3.2\times {10}^{-19}}{4.059\times {10}^{-26}}=7.9\times {10}^6{\text{ C kg}}^{-1}$

Worked Example 3 - Specific charge of an atom

The specific charge of atoms is zero because the net charge is zero.

This is because the number of electrons is equal to the number of protons in a neutral atom.