Kinetic energy formula for alpha particle speed

Steps:

• Mass of alpha particle is approximately $m = 6 \times 10^{-26}$ kg (4 times proton mass, approximated).
• Given kinetic energy $KE = 2 \times 10^{-12}$ J.
• Use $KE = \frac{1}{2} m v^2$, so $v=\sqrt{\frac{2\times KE}{m}}=\sqrt{\frac{4\times {}^{}}{}}$.
• Calculate: $\frac{4 \times 10^{-12}}{6 \times 10^{-26}} = 6.67 \times 10^{13}$, m/s.

Why C is correct:

• $8.1 \times 10^6$ m/s matches the result from $v = \sqrt{\frac{2KE}{m}}$ using the approximate mass of the alpha particle.

Why the others are wrong:

• A: Too low; results from using mass about 40 times larger than approximate value.
• B: Too low; results from using mass about 16 times larger than approximate value.
• D: Too high; results from using mass about 4 times smaller than approximate value.

Final answer: C