An alpha particle is emitted from a radioactive source with an energy of 5 MeV. How fast is it moving (in m/s)? (m = 4.002 603 u, 1 u = 1.66 × 10−²⁷ kg.) A) 2.4 × 10⁷ B) 1.6 × 10⁷ C) 3.7 × 10⁷ D) 4.6 × 10⁷ E) 2.1 × 10⁷

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Quizplus · Accepted Answer

To find the velocity of the alpha particle, we can use the kinetic energy formula: $KE = \frac{1}{2}mv^2$, where $m$ is the mass of the alpha particle and $v$ is its velocity. First, convert the mass of the alpha particle from atomic mass units (u) to kilograms (kg) using the given conversion factor $1 u = 1.66 \times 10^{-27} kg$. The mass of the alpha particle is $4.002603 u \times 1.66 \times 10^{-27} kg/u = 6.6442 \times 10^{-27} kg$. The energy given is 5 MeV, which needs to be converted to joules (J). $1 eV = 1.602 \times 10^{-19} J$, so $5 MeV = 5 \times 10^6 eV = 5 \times 10^6 \times 1.602 \times 10^{-19} J = 8.01 \times 10^{-13} J$. Solving the kinetic energy formula for $v$, we get $v = \sqrt{\frac{2KE}{m}} = \sqrt{\frac{2 \times 8.01 \times 10^{-13} J}{6.6442 \times 10^{-27} kg}} \approx 1.6 \times 10^{7} m/s$.

An Alpha Particle Is Emitted from a Radioactive Source with an Energy