First slide

Bohr's atom model

Question

Magnetic field at the center (at nucleus) of the hydrogen like atoms (atomic number = z) due to the motion of electron in $n^{t h}$ orbit is proportional to

Moderate

A

$\frac{n^{3}}{z^{5}}$
B

$\frac{n^{4}}{z}$
C

$\frac{z^{2}}{n^{3}}$
D

$\frac{z^{3}}{n^{5}}$

Solution

$B_{n} = \frac{μ_{0} I_{n}}{2 r_{n}} or B_{n} \propto \frac{I_{n}}{r_{n}} or B \propto \frac{(f_{n})}{r_{n}} ∴ B_{n} \propto \frac{(v_{n} / r_{n})}{r_{n}} Hence, B \propto \frac{v_{n}}{{(r_{n})}^{2}} \propto \frac{(z / n)}{{(n^{2} / z)}^{2}} \propto \frac{z^{3}}{n^{5}}$

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