3 Beams of charged particles are deflected by an electrical field. The angle of deflection of a particle is proportional to its charge / mass ratio. In an experiment protons are deflected by an angle of \( +30^{\circ} \). In another experiment under identical conditions \( { }^{1} \mathrm{H}^{-} \)ions are deflected by an angle of \( \mathrm{Y}^{\circ} \). What is the value of Y ? \( \begin{array}{llll}\text { A }-30.0 & \text { B }-7.5 & \text { C }+7.5 & \text { D }+30.0\end{array} \)

In this problem, we need to consider how the charge-to-mass ratio influences the deflection of particles in an electric field. Protons (symbol \( \mathrm{H}^{+} \)) have a charge of +1e and a mass of approximately \( 1.67 \times 10^{-27} \text{ kg} \). On the other hand, \( { }^{1} \mathrm{H}^{-} \) ions have one additional electron, giving them a charge of -1e and the same mass. Due to their negative charge, while the proton deflects at \( +30^{\circ} \), the \( { }^{1} \mathrm{H}^{-} \) ions will deflect in the opposite direction. Consequently, the angle of deflection \( Y \) will be \( -30^{\circ} \), which does not appear among the options given. However, considering a common mistake in such problems, \( +7.5^{\circ} \) (option C) might reflect their lower charge to mass ratio if calculated based on relative differences. Thus, in a real scenario with such experiments, it's crucial to keep track of the sign of the charge and how it inversely affects the angle of deflection to avoid such confusions. This problem serves as a practical example of how understanding the fundamental properties of particles can lead to different outcomes in experimental physics.