Understanding SI Base Units and Derived Units

The International System of Units (SI) defines seven base units for fundamental physical quantities. All other SI units are derived from these base units. The question asks us to identify which of the given options represents a quantity that does not have an SI base unit. This means we are looking for a quantity whose SI unit is a derived unit.

The Seven SI Base Quantities and Units

Here are the seven fundamental quantities and their corresponding SI base units:

Analyzing the Given Options

Let's examine each option provided in the question:

1. Amount of substance

Amount of substance is one of the seven SI base quantities. Its SI base unit is the mole (mol).

2. Frequency

Frequency is defined as the number of occurrences of a repeating event per unit of time. Mathematically, frequency (\(f\)) is the reciprocal of the period (\(T\)), which is the time duration of one cycle:

\[f = \frac{1}{T}\]

Since the period \(T\) is a measure of time, its unit is the second (s), which is an SI base unit for time. Therefore, the unit of frequency is:

\[\text{Unit of frequency} = \frac{1}{\text{Unit of time}} = \frac{1}{\text{second}} = \text{second}^{-1}\]

The special name for the unit second\(^{-1}\) is Hertz (Hz). Since the unit of frequency (Hertz or s\(^{-1}\)) is expressed in terms of a base unit raised to a power, it is a derived unit, not a base unit.

3. Luminous intensity

Luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle. It is one of the seven SI base quantities. Its SI base unit is the candela (cd).

4. Electric current

Electric current is defined as the rate of flow of electric charge through a surface. It is one of the seven SI base quantities. Its SI base unit is the ampere (A).

Conclusion

Based on the analysis:

• Amount of substance has the SI base unit mole (mol).
• Frequency has the SI derived unit Hertz (Hz), which is s\(^{-1}\).
• Luminous intensity has the SI base unit candela (cd).
• Electric current has the SI base unit ampere (A).

Therefore, Frequency is the quantity among the options that does not have an SI base unit; its unit is a derived unit.

Revision Table: SI Base Units vs. Derived Units

Understanding the difference between base and derived units is key to answering questions like this.

Additional Information on Physical Quantities and Units

Physical quantities are measurable properties of the physical world. To measure them, we use units. The SI system provides a coherent framework for measurement globally.

• Coherence: Derived units in the SI system are formed using simple mathematical relationships (multiplication, division, powers) between base units, without introducing numerical factors.
• Frequency Unit (Hertz): The Hertz (Hz) is named after Heinrich Hertz, who made significant contributions to the study of electromagnetic waves. 1 Hz means one cycle or occurrence per second.
• Importance of Base Units: The choice of base units is somewhat arbitrary but provides a practical and consistent foundation for all other measurements in science and engineering.