Question

If a proton, a deuteron and an $\alpha$-particle have the same speed, then the kinetic energy is

• A. same for all particles
• B. the lowest for proton
• C. the highest for deuteron
• D. same for proton and deuteron
• E. the lowest for $\alpha$-particle

Hint:

For same velocity: - Kinetic energy depends only on mass - Larger mass $\Rightarrow$ larger kinetic energy

Answer 1

The Correct Option is B

Concept: Kinetic energy is given by: \[ K = \frac{1}{2}mv^2 \] For same speed, kinetic energy is directly proportional to mass: \[ K \propto m \]

Step 1: Compare masses of particles.

• Proton mass $\approx m$
• Deuteron mass $\approx 2m$
• $\alpha$-particle mass $\approx 4m$

Step 2: Compare kinetic energies.
Since $K \propto m$: \[ K_{\text{proton}} < K_{\text{deuteron}} < K_{\alpha} \]

Step 3: Conclusion.
The proton has the least kinetic energy.