The magnetic field induction produced at the centre of orbit due to an...
The magnetic field induction produced at the centre of orbit due to an...
Explanation:
The magnetic field induction produced at the center of the orbit due to an electron revolving in the nth orbit of a hydrogen atom is given by the formula:
B = (μ₀ * e * v) / (4π * r)
Where:
- B is the magnetic field induction
- μ₀ is the permeability of free space
- e is the charge of the electron
- v is the velocity of the electron
- r is the radius of the orbit
The velocity of the electron in the nth orbit can be calculated using the formula:
v = (2π * r) / T
Where:
- T is the time period of revolution of the electron in the nth orbit
Now, let's analyze the options:
1) n-³:
If the magnetic field induction is proportional to n-³, it means that as the value of n increases, the magnetic field induction decreases. However, this is not the case. The magnetic field induction is not inversely proportional to the cube of n.
2) n-5:
If the magnetic field induction is proportional to n-5, it means that as the value of n increases, the magnetic field induction decreases rapidly. However, this is not the case. The magnetic field induction is not inversely proportional to the fifth power of n.
3) n5:
If the magnetic field induction is proportional to n5, it means that as the value of n increases, the magnetic field induction increases rapidly. However, this is also not the case. The magnetic field induction is not directly proportional to the fifth power of n.
4) n³:
If the magnetic field induction is proportional to n³, it means that as the value of n increases, the magnetic field induction increases. This is the correct option. The magnetic field induction is directly proportional to the cube of n. As the electron moves to higher orbits (higher values of n), the magnetic field induction at the center of the orbit increases.
Therefore, the correct answer is option 4) n³.
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