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Atoms and Nuclei question

2007 · Q125
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Atoms and Nuclei question

2007 · Q125

NEETPhysicsAtoms and NucleiMCQ+4 / −1
In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential VVV and then made to describe semicircular paths of radius R using a magnetic field B. If V and B are kept constant, the ratio (charg⁡e  on   the  ion  mass  of  the  ion)\left( {{{ch\arg e\,\,on\,\,\,the\,\,ion\,\,} \over {mass\,\,of\,\,the\,\,ion}}} \right)(massoftheionchargeontheion​) will be proportional to
  1. A
    1/R2
  2. B
    R2
  3. C
    R
  4. D
    1/R
View written solutionFree

Correct answer: A

In mass spectrometer, when ions are accelerated through potential V,

12mv2=qV{1 \over 2}m{v^2} = qV21​mv2=qV ....(1)

As the magnetic field curves the path of the ions in a semicircular orbit.

∴\therefore∴ Bqv = mv2R{{m{v^2}} \over R}Rmv2​

⇒\Rightarrow⇒ v = BqRm{{BqR} \over m}mBqR​ .....(2)

Now by substituting (ii) in (i),

12m(BqRm)2=q{1 \over 2}m{\left( {{{BqR} \over m}} \right)^2} = q21​m(mBqR​)2=q


⇒\Rightarrow⇒ qm=2VB2R2{q \over m} = {{2V} \over {{B^2}{R^2}}}mq​=B2R22V​

As V and B are constants,

∴\therefore∴ qm{q \over m}mq​ ∝\propto∝ 1R2{1 \over {{R^2}}}R21​

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