TG EAMCET 2 May 2025 Shift 1 Paper

When a charged particle moves in a magnetic field, the time it takes to make one full round (the time period) is given by:$T = \frac{2 \pi m}{B q}$Here, $m$ is the mass of the particle, $q$ is its charge, and $B$ is the magnetic field. This means the time period depends on the ratio of mass to charge ( $\; \frac{n}{c}$To compare the time periods of a proton ( $T_p$ ) and an alpha particle ( $T_\alpha$ ), use this ratio:$\; \frac{T_p}{T_\alpha} = \; \frac{m_p}{m_\alpha} \times \; \frac{q_\alpha}{q_p}$An alpha particle has a mass four times that of a proton ( $m_\alpha = 4 m_p$ ) and a charge twice that of a proton ( $q_\alpha = 2 q_p$ ).Plug these values in:$\; \frac{T_p}{T_\alpha} = \; \frac{m_p}{4 m_p} \times \; \frac{2 q_p}{q_p} = \; \frac{1}{4} \times 2 = \; \frac{1}{2}$This shows that the time taken by a proton is half that of the alpha particle. So, the ratio of their times is$T_p : T_\alpha = 1 : 2$