Solve using base units

May 27, 2026Chemistry

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Answer

\text{kg}^{-1} \text{A s}

4 steps

Define specific charge in terms of fundamental quantities.
Specific charge ( $\delta$ ) is defined as the ratio of charge ( $Q$ ) to mass ( $m$ ).
$\delta = \frac{Q}{m}$
Express charge in terms of base units.
Charge ( $Q$ ) is not a base unit. However, electric current ( $I$ ) is a base unit (Ampere, A), and current is defined as the rate of flow of charge ( $I = \frac{Q}{t}$ ).
Therefore, charge can be expressed as $Q = I \times t$ .
The base unit for current is Ampere (A).
The base unit for time is second (s).
So, the base unit for charge is Ampere-second (A s).
Express mass in terms of base units.
Mass ( $m$ ) is a base unit.
The base unit for mass is kilogram (kg).
Substitute the base units into the equation for specific charge.
$\delta = \frac{\text{base unit of charge}}{\text{base unit of mass}} = \frac{\text{Ampere} \cdot \text{second}}{\text{kilogram}}$ $\delta = \frac{\text{A} \cdot \text{s}}{\text{kg}}$
This can also be written as:
$\delta = \text{kg}^{-1} \cdot \text{A} \cdot \text{s}$
The base units of specific charge are $\text{kg}^{-1} \text{A s}$ .

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