A mass spectrometer applies a voltage of 2.00 kV to accelerate a singly charged positive ion. A magnetic field of B = 0.400 T then bends the

Question

A mass spectrometer applies a voltage of 2.00 kV to accelerate a singly charged positive ion. A magnetic field of B = 0.400 T then bends the ion into a circular path of radius 0.305 m. What is the mass of the ion?

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bonexptip 4 years 2021-08-01T05:45:35+00:00 1 Answers 46 views 0

Answers ( )

  1. Xavia
    0
    2021-08-01T05:47:12+00:00
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    The mass of the ion is 5.96 X 10⁻²⁵ kg

    Explanation:

    The electrical energy given to the ion Vq will be changed into kinetic energy \frac{1}{2}mv^2

    As the ion moves with velocity v in a magnetic field B then the magnetic Lorentz force Bqv will be balanced by centrifugal force \frac{mv^2}{r}.

    So,

    Vq = \frac{1}{2}mv^2

    and

    Bqv = \frac{mv^2}{r}

    Right from these eliminating v, we can derive

    m = \frac{B^2r^2q}{2V}

    On substituting the value, we get:

    m = \frac{(0.4)^2X (0.305)^2 X1.602X 10^-^1^9}{2X 2000}\\\\

    m = 5.96 X 10⁻²⁵ kg.

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