Question:
Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the 2nd and 4th orbits of a hydrogen atom.
Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the 2nd and 4th orbits of a hydrogen atom.
Updated On: Apr 10, 2026
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Correct Answer: 4
Solution and Explanation
Step 1: Understanding the question.
The magnetic field generated by the motion of an electron in an orbit is proportional to the current produced by the motion of the electron. The current \( I \) is related to the angular momentum \( L \) of the electron, and the magnetic field generated by a moving charge in an orbit is given by the formula: \[ B = \frac{\mu_0 I}{2r}. \] Where \( r \) is the radius of the orbit.
Step 2: Magnetic field due to electron in the 2nd and 4th orbits.
Using Bohr's model, the radius \( r_n \) of the nth orbit of a hydrogen atom is given by: \[ r_n = n^2 \cdot r_1, \] where \( r_1 = 0.529 \times 10^{-10} \) m is the radius of the first orbit, and \( n \) is the principal quantum number. For the 2nd orbit: \[ r_2 = 2^2 \cdot r_1 = 4r_1. \] For the 4th orbit: \[ r_4 = 4^2 \cdot r_1 = 16r_1. \]
Step 3: Relating magnetic fields.
The magnetic field is inversely proportional to the radius of the orbit, so the ratio of magnetic fields at the 2nd and 4th orbits is: \[ \frac{B_2}{B_4} = \frac{r_4}{r_2} = \frac{16r_1}{4r_1} = 4. \] Thus, the ratio of the magnetic fields is: \[ \boxed{4}. \]
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