Question 614: Atoms & Nuclei

Question

In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential $$V$$ and then made to describe semicircular paths of radius R using a magnetic field B. If V and B are kept constant, the ratio $$\left( {{{ch\arg e\,\,on\,\,\,the\,\,ion\,\,} \over {mass\,\,of\,\,the\,\,ion}}} \right)$$ will be proportional to

Accepted Answer

In mass spectrometer, when ions are
accelerated through potential V,
$${1 \over 2}m{v^2} = qV$$ ....(1)
As the magnetic field curves the path of the
ions in a semicircular orbit.
$$ 	herefore $$ Bqv = $${{m{v^2}} \over R}$$
$$ \Rightarrow $$ v = $${{BqR} \over m}$$ .....(2)
Now by substituting (ii) in (i),
$${1 \over 2}m{\left( {{{BqR} \over m}} ight)^2} = q$$
$$ \Rightarrow $$ $${q \over m} = {{2V} \over {{B^2}{R^2}}}$$
As V and B are constants,
$$ 	herefore $$ $${q \over m}$$ $$ \propto $$ $${1 \over {{R^2}}}$$

Answer

1/R2

Answer

R2

Answer

R

Answer

1/R

Atoms & Nuclei

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