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  • Please,please help me If one were to apply Bohr model to a particle of mass '‘m'’ and charge '‘q’ 'moving in a plane under the influence of a magnetic field '‘B'’, the energy of the charged particle in the nth level will

 If one were to apply Bohr model to a particle of mass 'm' and charge 'q 'moving in a plane under the influence of a magnetic field 'B', the energy of the charged particle in the nth level will be :

  • Option 1)

    n\left ( \frac{hqB}{2\pi m} \right )

  • Option 2)

    n\left ( \frac{hqB}{4\pi m} \right )

  • Option 3)

    n\left ( \frac{hqB}{8\pi m} \right )

  • Option 4)

    n\left ( \frac{hqB}{\pi m} \right )

 

Answers (1)

best_answer

As we learnt in

Hypothetical atomic model -

\left | \frac{dU}{dr} \right |= \frac{mv^{2}}{r}

mvr= \frac{nh}{2\pi }

- wherein

Solve these two equations to get radius and energy of hypothetical atoms

 

 Under magnetic field 

qvB=\frac{mv^{2}}{r}        or      mv = 2Br                                     (1)

Also from Bohr's quantisation principle 

mvr=\frac{nh}{2\pi}          or        vr=\frac{nh}{2\pi m}                            (2)

Multiply equation (1) & (2) 

mv^{2}r=qBr.\frac{nh}{2\pi m}

mv^{2}=n \left[\frac{qBh}{2\pi m} \right ]

So kinetic energy =\frac{1}{2}mv^{2}

E=n \left[\frac{qBh}{4\pi m} \right ]

Correct option is 2.


Option 1)

n\left ( \frac{hqB}{2\pi m} \right )

This is an incorrect option.

Option 2)

n\left ( \frac{hqB}{4\pi m} \right )

This is the correct option.

Option 3)

n\left ( \frac{hqB}{8\pi m} \right )

This is an incorrect option.

Option 4)

n\left ( \frac{hqB}{\pi m} \right )

This is an incorrect option.

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