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 hydrogen atom

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 hydrogen atom _________. [2026]

Smart Achievers · Accepted Answer

(64)

$The magnetic field due to circular loop, B = \frac{μ_{0} I}{2 π r}$

$Current due to orbiting electron, I = \frac{e v}{2 π r}$

$\Rightarrow B \propto \frac{v}{r^{2}}$

$But, v \propto \frac{Z}{n} and r \propto \frac{n^{2}}{Z}$

$\Rightarrow B \propto \frac{(\frac{Z}{n})}{{(\frac{n^{2}}{Z})}^{2}} = \frac{Z^{3}}{n^{5}}$

$\frac{B_{1}}{B_{2}} = \frac{n_{2}^{5}}{n_{1}^{5}} = \frac{4^{5}}{2^{5}} = 64$

Solution

Q.
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 hydrogen atom _________. [2026]

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Solution

Q. 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 hydrogen atom _________. [2026]

Ans. (64) The magnetic field due to circular loop, B=μ0I2πr Current due to orbiting electron, I=ev2πr ⇒B∝vr2 But, v∝Zn and r∝n2Z ⇒B∝(Zn)(n2Z)2=Z3n5 B1B2=n25n15=4525=64

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Q.
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 hydrogen atom _________. [2026]