Magnetic Effects & Magnetism

JEE Main level, single correct, medium

118 of 276

Question 118 of 276

An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr's quantization is applicable, then the radius of the electronic orbit in the first excited state is :

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Answer: (A) hπeB\sqrt{\frac{\mathrm{h}}{\pi \mathrm{eB}}}

mvr=nh2πm v r=\frac{n h}{2 \pi} ...(i)
r=vmBqr=\frac{v m}{B q} ....(ii)
n=2mr(rBqm)=2h2πr=hπBqq=er=hπBe\begin{aligned} & n=2 \\ & m r\left(\frac{r B q}{m}\right)=\frac{2 h}{2 \pi} \\ & r=\sqrt{\frac{h}{\pi B q}} \\ & q=e \\ & r=\sqrt{\frac{h}{\pi B e}}\end{aligned}

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