An a particle, 4He2 + , has a mass of 4.00151 amu. Find the value of its charge-to-mass ratio in C/kg.

Verified step by step guidance

1. Identify the charge of the \( \alpha \) particle: An \( \alpha \) particle is essentially a helium nucleus, which consists of 2 protons and 2 neutrons. The charge of the \( \alpha \) particle is therefore the charge of 2 protons.
2. Calculate the charge in coulombs: The charge of a single proton is approximately \( 1.602 \times 10^{-19} \) C. Therefore, the charge of the \( \alpha \) particle is \( 2 \times 1.602 \times 10^{-19} \) C.
3. Convert the mass from atomic mass units (amu) to kilograms: The mass of the \( \alpha \) particle is given as 4.00151 amu. Use the conversion factor \( 1 \text{ amu} = 1.660539 \times 10^{-27} \text{ kg} \) to convert the mass to kilograms.
4. Calculate the charge-to-mass ratio: Divide the total charge of the \( \alpha \) particle by its mass in kilograms to find the charge-to-mass ratio.
5. Express the charge-to-mass ratio in \( \text{C/kg} \): Ensure the final expression of the charge-to-mass ratio is in the correct units of \( \text{C/kg} \).

Key Concepts

Charge-to-Mass Ratio

The charge-to-mass ratio (q/m) is a measure of the amount of charge per unit mass of a particle. It is calculated by dividing the charge of the particle (in coulombs) by its mass (in kilograms). This ratio is crucial in fields like mass spectrometry and particle physics, as it helps in understanding the behavior of charged particles in electric and magnetic fields.

Units of Measurement

In chemistry and physics, it is essential to use consistent units when performing calculations. The charge is typically measured in coulombs (C), while mass is measured in kilograms (kg). Understanding how to convert between units, such as converting atomic mass units (amu) to kilograms, is vital for accurately calculating the charge-to-mass ratio.

Helium Ion (4He2+)

The helium ion (4He2+) is a positively charged ion of helium, which has lost two electrons, resulting in a charge of +2. Its mass is slightly greater than that of a neutral helium atom due to the presence of two protons and two neutrons. Recognizing the properties of this ion, including its charge and mass, is essential for calculating its charge-to-mass ratio.