A) the path of electron is less curved
B) the path of proton is less curved
C) both have equal curved paths
D) both have straight line paths
Correct Answer: B
Solution :
Kinetic energy of proton = Kinetic energy of electron \[\frac{1}{2}{{m}_{p}}v_{p}^{2}=\frac{1}{2}{{m}_{e}}v_{e}^{2}\] \[\Rightarrow \] \[\frac{{{m}_{p}}}{{{m}_{e}}}={{\left( \frac{{{v}_{e}}}{{{v}_{p}}} \right)}^{2}}\] ?..(i) If B is the strength of the magnetic field and m, v and q, the mass, velocity and charge of the positive ion, then \[Bqv=\frac{m{{v}^{2}}}{r}\] As \[{{q}_{p}}={{q}_{e}}\] and B is same for both electron and proton \[r=mv\] \[\therefore \] \[\frac{{{r}_{e}}}{{{r}_{p}}}=\frac{{{m}_{e}}{{v}_{e}}}{{{m}_{p}}{{v}_{p}}}\] ?..(ii) From Eqs. (i) and (ii) \[\frac{r_{e}^{2}}{r_{p}^{2}}=\frac{{{m}_{e}}}{{{m}_{p}}}\] \[\therefore \] \[{{r}^{2}}\propto m\] Mass of a' proton is more than that of electron. Therefore, radius of proton will be more. Hence, the path of proton will be less curved.
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