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An electron rotates in a circle around a...

An electron rotates in a circle around a nucleus with positive charge `Ze`. How is the electrons'velocity realted to the radius of its orbit?

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To find the relationship between the electron's velocity and the radius of its orbit when it is rotating around a nucleus with a positive charge \( Ze \), we can follow these steps: ### Step 1: Understand the forces acting on the electron The electron experiences a centripetal force due to the electrostatic attraction between the positively charged nucleus and the negatively charged electron. This force can be expressed using Coulomb's law. ### Step 2: Write down Coulomb's Law The electrostatic force \( F \) between the nucleus and the electron is given by: \[ ...
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A particle of charge equal to that of electron and mass 208 times the mass of the electron moves in a circular orbit around a nucleus of charge +3e. Assuming that the Bohr model of the atom is applicable to this system find the value of n for which the radius of the orbit is approximately the same as that of the first Bohr orbit of the hydrogen atom.

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Knowledge Check

  • An electron orbiting around the nucleus of an atom

    A
    has a magnetic dipole moment
    B
    exerts an electric force on the nucleus equal to that on it by the nucleus
    C
    does produce a magnetic induction at the nucleus
    D
    has a net energy inversely proportional to its distance from the nucleus.

  • An electron orbiting around a nucleus has angular momentum L. The magnetic field produced by the electron at the centre of the orbit can be expressed as :

    A
    `B = (mu_(0) e//8pi mr^(3))L`
    B
    `B =(mu_(0)e//4 pi mr^(3))L`
    C
    `B = (mu_(0) e//pi mr^(3))L`
    D
    `B =(e//4 pi epsilon_(0) mr^(3))L`

  • An electron of charge 'e' is revolving in a circular orbit of radius r around a nucleus with speed v. The equivalent current is

    A
    `2e pi r v`
    B
    e vr
    C
    `(ev)/(2 pi r)`
    D
    zero

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