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NEET 2007 (AIPMT) · Quantum Numbers, X-rays & Other Questions

Quantum Numbers, X-rays & Other Questions question from NEET 2007 (AIPMT)

Q8NEET 2007 · AIPMTMedium

Quantum Numbers, X-rays & Other Questions

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

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Answer: (a)

  1. Acceleration: qV=12mv2⇒v=2qVmqV = \frac{1}{2}mv^2 \Rightarrow v = \sqrt{\frac{2qV}{m}}
  2. Circular path: R=mvqB=1B2mVqR = \frac{mv}{qB} = \frac{1}{B}\sqrt{\frac{2mV}{q}}
  3. qm=2VB2R2∝1R2\frac{q}{m} = \frac{2V}{B^2R^2} \propto \frac{1}{R^2}
  4. So the answer is (a) 1/R21/R^2.
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