Find the ratio of specific charges of an α-particle and a deuteron.

The specific charge of a particle is defined as the charge of the particle divided by its mass. To find the ratio of the specific charges of an α-particle and a deuteron, we first need to know their charges and masses.

Understanding the Particles

An α-particle consists of 2 protons and 2 neutrons, while a deuteron consists of 1 proton and 1 neutron.

Charge and Mass Values

• Charge of α-particle: +2e (where e is the elementary charge, approximately 1.6 x 10^-19 C)
• Mass of α-particle: Approximately 4 u (atomic mass units)
• Charge of deuteron: +1e
• Mass of deuteron: Approximately 2 u

Calculating Specific Charges

The specific charge can be calculated using the formula:

Specific Charge = Charge / Mass

For the α-particle:

Specific Charge_α = (2e) / (4 u) = 0.5 e/u

For the deuteron:

Specific Charge_d = (1e) / (2 u) = 0.5 e/u

Finding the Ratio

Now, we can find the ratio of the specific charges:

Ratio = Specific Charge_α / Specific Charge_d = (0.5 e/u) / (0.5 e/u) = 1

Final Result

The ratio of the specific charges of an α-particle to a deuteron is 1. This means they have the same specific charge.