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AQA A-Level Physics Notes

1.1.1 Fundamental Units

Introduction to SI Units

The International System of Units (SI) provides a standard for scientific measurements worldwide. This system is based on seven fundamental units, from which all other units are derived. Understanding these units is crucial for accurately measuring and interpreting physical phenomena.

Understanding Mass

Mass, a measure of the amount of matter in an object, is fundamental to the study of physics. It is a critical factor in understanding concepts like inertia, gravitational force, and energy.

SI Unit for Mass: Kilogram (kg)

  • Definition: The kilogram is defined by setting the Planck constant to be exactly 6.62607015×10⁻³⁴ kg⋅m²/s. This definition connects the mass unit directly to fundamental constants of nature.
  • Applications: Mass is used in laws of motion, energy calculations, and understanding gravitational interactions.

Understanding Length

Length is a measure of distance. In physics, it's essential for calculating areas, volumes, understanding waves, and describing the motion of objects.

SI Unit for Length: Meter (m)

  • Definition: The meter is defined as the distance travelled by light in a vacuum in 1/299,792,458 of a second. This definition links length to the fundamental properties of the universe.
  • Applications: It is used in geometrical measurements, determining distances in space, and in the study of wave phenomena.

Understanding Time

Time, a fundamental continuous sequence, is critical for understanding motion, rates of changes, and the dynamics of physical systems.

SI Unit for Time: Second (s)

  • Definition: The second is defined by the transition frequency of cesium atoms, specifically the radiation corresponding to the transition between two hyperfine levels of the ground state of cesium-133.
  • Applications: Time is used in calculating speeds, understanding phenomena in quantum mechanics, and in the study of relativity.

Amount of Substance

In both physics and chemistry, the amount of substance is a measure of the number of entities (atoms, molecules, ions, etc.) present in a material.

SI Unit for Amount of Substance: Mole (mol)

  • Definition: The mole is defined by fixing the Avogadro constant at exactly 6.02214076×10²³ entities per mole.
  • Applications: This unit is essential in stoichiometry, chemical reactions, and understanding the properties of gases.

Understanding Temperature

Temperature is a measure of thermal energy within a system, directly relating to the kinetic energy of particles.

SI Unit for Temperature: Kelvin (K)

  • Definition: The Kelvin scale starts at absolute zero, the point where all molecular motion ceases, and is defined by setting the Boltzmann constant to 1.380649×10⁻²³ J/K.
  • Applications: Temperature is crucial in thermodynamics, studying phase changes, and understanding heat transfer.

Understanding Electric Current

Electric current, the flow of electric charge, is central to the study of electromagnetism and electrical circuits.

SI Unit for Electric Current: Ampere (A)

  • Definition: The ampere is defined by fixing the elementary charge to be exactly 1.602176634×10⁻¹⁹ coulombs.
  • Applications: It's essential in understanding electrical circuits, magnetic fields, and in the practical implementation of electrical devices.

Exclusion of the Candela

While the candela is a fundamental SI unit, it is specific to photometry and thus not included in this basic physics module.

  • Candela: The candela measures luminous intensity, a different aspect of light compared to the physical properties discussed here.

FAQ

The significance of defining the ampere in terms of the elementary charge lies in its precision and universality. The elementary charge is a fundamental physical constant, representing the electric charge carried by a single proton. By linking the ampere (the unit of electric current) to this constant, the definition becomes more accurate and less dependent on physical artifacts or specific experimental setups. The current definition, established in 2019, sets the ampere as the constant current which, if maintained in two straight parallel conductors of infinite length and negligible circular cross-section, placed one meter apart in a vacuum, would produce a force equal to 2×10⁻⁷ newton per meter of length. This redefinition ties the ampere directly to the charge of an electron, making it a more fundamental and reproducible standard. It reflects the ongoing effort in physics to base units on unchanging properties of nature, thereby enhancing the precision and reliability of measurements.

In scientific contexts, temperature is measured in Kelvin for several reasons. Firstly, the Kelvin scale is an absolute temperature scale, starting at absolute zero, the theoretical point where all molecular motion ceases. This zero point provides a clear and universal baseline, making Kelvin ideal for scientific calculations. In contrast, the Celsius and Fahrenheit scales are relative scales, based on arbitrary points such as the freezing and boiling points of water. Secondly, the Kelvin scale is directly related to the average kinetic energy of particles, which is fundamental to thermodynamics. This makes it more straightforward to use in scientific equations, particularly those involving the laws of thermodynamics. The unit increments in the Kelvin scale are the same as those in Celsius, which makes conversions between these scales simple. Overall, Kelvin provides a more scientifically rigorous and universally applicable scale for temperature measurement.

The accurate measurement of the mole, the SI unit for the amount of substance, is crucial in various practical applications, most notably in chemistry and pharmacology. In chemistry, the mole allows scientists to quantify the exact amounts of substances needed for reactions, ensuring precision in formulations and predicting reaction outcomes. This is vital in the synthesis of chemicals, materials, and pharmaceuticals. In pharmacology, the mole is fundamental for dosing medications accurately, ensuring efficacy and safety. The redefinition of the mole in terms of Avogadro's number, a fundamental constant, in 2019, provided a more stable and precise standard. This redefinition ties the mole to a fixed number of specified particles, making it independent of the mass of a specific substance. This ensures that the mole remains constant over time and universally applicable, which is crucial for international scientific and industrial collaborations. Accurate mole measurements underpin essential processes ranging from manufacturing to healthcare, highlighting the profound impact of this unit on both science and everyday life.

The second, the SI unit for time, is defined with exceptional precision based on the properties of caesium atoms. Specifically, it's determined by the frequency of radiation emitted during the transition between two hyperfine levels of the ground state in a caesium-133 atom. This definition was adopted in 1967, thanks to the development of atomic clocks, which allowed for extremely precise measurements. The exact definition is: one second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between these two hyperfine levels. This method of defining a second harnesses fundamental properties of quantum mechanics, ensuring that the unit of time is constant and not subject to variation, unlike earlier methods based on astronomical observations. This atomic definition exemplifies the intersection of advanced physics and time measurement, reflecting our deepening understanding of the natural world.

The kilogram is unique among SI base units as it is the only one incorporating a prefix ('kilo') in its name. This anomaly dates back to the French Revolution when the metric system was first established. Originally, the 'gram' was defined as the base unit of mass. However, it was soon realized that a gram was too small for practical purposes, especially in commerce and everyday use. Consequently, the 'kilogram', equal to 1000 grams, was introduced as a more convenient measure. When the SI system was formalized in 1960, it inherited this convention. The kilogram remains the base unit for mass instead of the gram, preserving historical continuity and avoiding disruption that would accompany redefining a widely used unit. This decision illustrates the balance between scientific precision and practical usability in standard measurements.

Practice Questions

Calculate the energy, in joules, of a photon with a frequency of 6.0 × 10¹⁴ Hz. (Note: The value of Planck’s constant is 6.63 × 10⁻³⁴ Js.)

The energy of a photon is calculated using the formula E = hf, where E is the energy, h is Planck's constant, and f is the frequency. Substituting the given values, E = 6.63 × 10⁻³⁴ Js × 6.0 × 10¹⁴ Hz = 3.978 × 10⁻¹⁹ J. Therefore, the energy of the photon is 3.978 × 10⁻¹⁹ joules. This calculation demonstrates an understanding of the relationship between energy and frequency in the context of quantum physics, a key concept in A-level Physics.

A student measures the length of a laboratory bench and records it as 2.5 meters. If the actual length of the bench is 2.52 meters, calculate the percentage error in the student's measurement.

The percentage error in a measurement is calculated using the formula: Percentage Error = (|Actual Value - Measured Value| / Actual Value) × 100%. Substituting the given values, Percentage Error = (|2.52m - 2.5m| / 2.52m) × 100% = (0.02m / 2.52m) × 100% = 0.7937%. Therefore, the percentage error in the student's measurement is approximately 0.79%. This calculation reflects the student's ability to apply mathematical concepts to practical measurement scenarios, an important skill in A-level Physics.

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