| An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii \[{{r}_{e}},\,\,{{r}_{p}},\,\,{{r}_{\alpha }}\] respectively in a uniform magnetic field B. |
| The relation between \[{{r}_{e}},\,\,{{r}_{p}},\,\,{{r}_{\alpha }}\] is: [JEE Main Online 08-04-2018] |
A) \[{{r}_{e}}<{{r}_{p}}<{{r}_{\alpha }}\]
B) \[{{r}_{e}}<{{r}_{\alpha }}<{{r}_{p}}\]
C) \[{{r}_{e}}>{{r}_{p}}={{r}_{\alpha }}\]
D) \[{{r}_{e}}<{{r}_{p}}={{r}_{\alpha }}\]
Correct Answer: D
Solution :
| [d] \[r=\frac{mv}{Bq}=\frac{\sqrt{2mk}}{Bq}\] |
| \[\frac{{{r}_{p}}}{{{r}_{e}}}=\frac{\sqrt{{{m}_{p}}}}{\sqrt{{{m}_{e}}}}\] \[{{m}_{p}}>{{m}_{e}}\] |
| \[{{r}_{p}}>{{r}_{e}}\] |
| \[\frac{{{r}_{p}}}{{{r}_{\alpha }}}=\frac{\sqrt{{{m}_{p}}}}{{{q}_{p}}}\frac{2{{q}_{p}}}{\sqrt{4{{m}_{p}}}}=1\] |
| \[{{r}_{p}}={{r}_{\alpha }}\] |
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