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Atoms & Nuclei

JEE Main level, numerical answer, medium

29 of 239

Question 29 of 239

Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the $2^{\text{nd}}$ and $4^{\text{th}}$ orbits of hydrogen atom _______.

Show answer and solution

Answer: 32

The magnetic field at the center of a circular orbit is given by

B = \dfrac{\mu_0 I}{2r}

.

The equivalent current due to the revolving electron is

I = \dfrac{e}{T} = \dfrac{ev}{2\pi r}

.

Substituting

I

into the expression for

B

, we get

B = \dfrac{\mu_0 ev}{4\pi r^2}

.

According to Bohr's model for a hydrogen atom, the velocity of the electron in the

n^{\text{th}}

orbit is

v \propto \dfrac{1}{n}

and the radius of the orbit is

r \propto n^2

.

Therefore, the magnetic field

B

depends on the principal quantum number

n

B \propto \dfrac{1/n}{(n^2)^2} \Rightarrow B \propto \dfrac{1}{n^5}

.

The ratio of the magnetic fields in the

2^{\text{nd}}

and

4^{\text{th}}

orbits is

\dfrac{B_2}{B_4} = \left(\dfrac{n_4}{n_2}\right)^5 = \left(\dfrac{4}{2}\right)^5 = 2^5 = 32

.

Answer:

32

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JEE Main Physics practice question on Atoms & Nuclei (Bohr's Atomic Model), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.

Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the 2nd2^{\text{nd}}2nd and 4th4^{\text{th}}4th orbits of hydrogen atom _______.

JEE Main question paper PDF

More Physics practice

Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the $2^{\text{nd}}$ and $4^{\text{th}}$ orbits of hydrogen atom _______.