Animated Solution for Physics - Atoms and Nuclei: At a specific instant, emission of radioactive compound is deflected in a magnetic field. The compound can emit (i) electrons (ii) protons (iii) He${}^{2+}$ (iv) neutrons The emission at the instant can be

Imagine you are observing a radioactive compound safely enclosed in a lead block with a tiny opening. This compound is actively emitting a stream of various particles. Now, suppose we place a strong, uniform magnetic field across the path of these emissions. What happens next is a beautiful demonstration of electromagnetism in action.

To understand the behavior of these particles, we must invoke the Lorentz Force Law. The magnetic force $\vec{F}$ experienced by a particle moving with velocity $\vec{v}$ in a magnetic field $\vec{B}$ is given by the master equation:

The most crucial variable in this equation is $q$, the electric charge of the particle. If a particle has no charge ($q=0$), the magnetic force is exactly zero, regardless of how fast it is moving or how strong the magnetic field is.

Let's evaluate the particles mentioned in our problem to see who gets deflected and who passes through undisturbed:

1. Electrons ($e^{-}$): These are fundamental particles carrying a negative elementary charge ($q=-e$). 2. Protons ($p^{+}$): These are the positively charged building blocks of nuclei ($q=+e$). 3. He${}^{2+}$ Ions: Also known as alpha particles, these are helium nuclei stripped of their electrons, carrying a double positive charge ($q=+2e$). 4. Neutrons ($n^0$): As their name implies, these particles are electrically neutral ($q=0$).

When this mixed stream of particles enters the magnetic field, the Lorentz force acts as a strict sorter.

Because the electron, proton, and He${}^{2+}$ ion all possess a non-zero electric charge, they will experience a magnetic force perpendicular to their velocity. This force acts as a centripetal force, causing their straight paths to bend into circular arcs. Interestingly, because the electron is negatively charged while the proton and He${}^{2+}$ are positively charged, the electron will deflect in the exact opposite direction to the other two!

On the other hand, the neutron has a charge of zero. Plugging $q=0$ into our Lorentz force equation yields $\vec{F}=0$. The neutron is completely oblivious to the magnetic field and continues on its straight, undeflected path.

The question asks which emissions can be deflected. Based on our analysis, any particle with a net charge will be deflected. Therefore, the electrons (i), protons (ii), and He${}^{2+}$ ions (iii) will all experience deflection.

This perfectly aligns with option (a). It is a brilliant reminder that magnetic fields are the ultimate detectors of electric charge, allowing us to separate and identify the invisible fragments of the atomic world.