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  • A single charged ion has a mass of   g. It is accelerated through a potential difference of 500 V&nb

A single charged ion has a mass of  1.13 \times 10^{-23} g. It is accelerated through a potential difference of 500 V and then enters a magnetic field of  0.4 \mathrm{~T} moving perpendicular to the field. The radius of its path in the field is

Option: 1

2.1 cm


Option: 2

2.1 mm


Option: 3

1.17 m


Option: 4

2.0 m


Answers (1)

best_answer

\mathrm{\frac{1}{2} m v^2=e V \text { or } v=\sqrt{\frac{2 e V}{m}} }
Also   \mathrm{\quad B e V=\frac{m v^2}{r} ~or !~v=\frac{B e r}{m} }
Equating (1) and (2), we get
\mathrm{ r=\frac{1}{B} \sqrt{\frac{2 m V}{e}} } 
Given \mathrm{ e=1.6 \times 10^{-19} \mathrm{C} }  (singly charged ion),\mathrm{ B= 0.4 \mathrm{~T}, V=500 \mathrm{~V} } and \mathrm{ m=1.13 \times 10^{-26} \mathrm{~kg} } .

Using these values in (3), we get \mathrm{ r=0.021 \mathrm{~m}=2.1 \mathrm{~cm} }  which is choice (a).

Posted by

shivangi.bhatnagar

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