Smoke Detector Calibration · AI Generator #GEN-2084CA74

Physics · modern-physics

Problem

A smoke detector uses americium-241, which emits alpha particles with energy Eα=5.5  MeVE_\alpha = 5.5\;\text{MeV}. When smoke particles enter the detector chamber, they absorb some alpha particles, reducing the detector current. An engineer needs to determine the alpha particle velocity for calibration purposes. Given that an alpha particle consists of 2 protons and 2 neutrons, and the proton mass is mp=1.67×10−27  kgm_p = 1.67 \times 10^{-27}\;\text{kg}, find the velocity of the alpha particles emitted by the americium-241 source. Note: 1  eV=1.60×10−19  J1\;\text{eV} = 1.60 \times 10^{-19}\;\text{J}
Intuitive explanation

The key is converting the alpha particle's kinetic energy from MeV into joules, then using the non-relativistic kinetic energy formula to solve for velocity. Since the alpha mass is roughly four times the proton mass, you'll first calculate the total mass, then rearrange Ek=12mv2E_k = \frac{1}{2}mv^2 to isolate vv—a straightforward energy-to-motion bridge that's essential for detector calibration.

Intuitive explanation

The key is converting the alpha particle's kinetic energy from MeV into joules, then using the non-relativistic kinetic energy formula to solve for velocity. Since the alpha mass is roughly four times the proton mass, you'll first calculate the total mass, then rearrange Ek=12mv2E_k = \frac{1}{2}mv^2 to isolate vv—a straightforward energy-to-motion bridge that's essential for detector calibration.

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