Question

Define specific charge of an electron.

Short answer

The specific charge of an electron is approximately \( -1.758 \times 10^{11} \text{ C/kg} \).

Step-by-step solution

Identify the charge of an electron

The charge of an electron is a fundamental physical constant symbolized as \(e\). The value of the electron charge is approximately \[e = -1.602 \times 10^{-19} \text{ coulombs} \]

Identify the mass of an electron

The mass of an electron is another fundamental constant, often symbolized as \(m_{e}\). The mass of an electron is approximately \[m_{e} = 9.109 \times 10^{-31} \text{ kilograms} \]

Define specific charge

The specific charge is defined as the charge-to-mass ratio. For an electron, it can be calculated using the formula: \[ \text{Specific charge} = \frac{\text{Charge of electron}}{\text{Mass of electron}} = \frac{e}{m_{e}} \]

Calculate the specific charge

Inserting the known values of the electron charge and mass, the specific charge of the electron can be calculated as follows: \[ \text{Specific charge} = \frac{-1.602 \times 10^{-19} \text{ C}}{9.109 \times 10^{-31} \text{ kg}} \] Simplifying this, we get approximately: \[ \text{Specific charge} = -1.758 \times 10^{11} \text{ C/kg} \]

Key concepts

charge of an electron

The charge of an electron is one of the fundamental constants in physics. Represented by the symbol \(e\), its value is about \( -1.602 \times 10^{-19} \) coulombs.
This means every electron carries a small but constant electric charge.
Keep in mind that this charge is negative, making electrons a vital part of electric currents and negative ion formation.
Understanding the electron charge helps in many areas of physics and chemistry.

mass of an electron

The mass of an electron is another crucial physical constant. Electron mass, denoted by the symbol \(m_{e}\), is approximately \( 9.109 \times 10^{-31} \) kilograms.
Though this mass is incredibly small, it's essential for calculations in atomic physics and quantum mechanics.
Electrons' mass, while minute compared to protons and neutrons, significantly influences atoms' behavior.

charge-to-mass ratio

The charge-to-mass ratio, also known as specific charge, is a measure of how much charge an electron carries relative to its mass.
It's defined as the electron charge divided by its mass:
\( \text{Specific charge} = \frac{e}{m_{e}} \).
For an electron, this value is roughly \( -1.758 \times 10^{11} \) coulombs per kilogram (C/kg).
This high specific charge indicates that electrons, despite their small mass, carry a notable amount of charge.
This concept is vital for understanding phenomena in electromagnetism and particle physics.