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 - Physics MCQ Physics | ExamTest.live

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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 semi-circular paths of radius R using a magnetic field B . If V and B are kept constant, the ratio \frac{q}{m} will be proportional to:

A $1/ R$
B $1/ R^{2}$
C $R^{2}$
D $R$

Solution & Step-by-step Explanation

Kinetic energy after acceleration: \frac{1}{2} m v^{2} = q V ⟹ v = \frac{2 q V}{m} .In magnetic field: R = \frac{m v}{qB} .Substitute v : R = \frac{m}{qB} \frac{2 q V}{m} = \frac{1}{B} \frac{2 mV}{q} R^{2} = \frac{2 mV}{q B ^{2}} ⟹ \frac{q}{m} = \frac{2 V}{B ^{2} R ^{2}} Since V and B are constant, \frac{q}{m} \propto \frac{1}{R ^{2}} .

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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 semi-circular paths of radius R using a magnetic field B . If V and B are kept constant, the ratio \frac{q}{m} will be proportional to:

1/ R

1/ R^{2}

R^{2}

R

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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 semi-circular paths of radius $R$ using a magnetic field $B$ . If $V$ and $B$ are kept constant, the ratio $\frac{q}{m}$ will be proportional to:

Solution & Step-by-step Explanation

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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 semi-circular paths of radius R using a magnetic field B. If V and B are kept constant, the ratio mq​ will be proportional to:

Solution & Step-by-step Explanation

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Discussion

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 semi-circular paths of radius $R$ using a magnetic field $B$ . If $V$ and $B$ are kept constant, the ratio $\frac{q}{m}$ will be proportional to: