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  • An α-particle moves in a circular path of radius 0.83 cm in the presence of a magnetic field of . The

An α-particle moves in a circular path of radius 0.83 cm in the presence of a magnetic field of \mathrm{0.25 ~Wb/m^2} . The wavelength associated with the particle will be :

Option: 1

\mathrm{1 \AA}


Option: 2

\mathrm{0.1 \AA}


Option: 3

\mathrm{10 \AA}


Option: 4

\mathrm{0.01 \AA}


Answers (1)

best_answer

Wavelength
\lambda=\frac{\mathrm{h}}{\mathrm{p}} \Rightarrow \lambda=\frac{\mathrm{h}}{\mathrm{mv}},

\mathrm{ h=\text { plank's constant }=6.63 \times 10^{-34} \mathrm{~J} . \mathrm{S} }
For circular motion = \mathrm{ F_c } = qvB
\mathrm{ \Rightarrow \frac{\mathrm{mv}^2}{\mathrm{r}}=\mathrm{qvB} \Rightarrow \frac{\mathrm{mv}}{\mathrm{qB}}=\mathrm{r} \\ }
\mathrm{ \mathrm{r}=\frac{\mathrm{mv}}{\mathrm{qB}} \Rightarrow m v=q r B \\ }
\mathrm{ \Rightarrow(2 e)\left(0.83 \times 10^{-2}\right)\left(\frac{1}{4}\right) }

\mathrm{ \lambda=\frac{6.6 \times 10^{-34} \times 4}{2 \times 1.6 \times 10^{-19} \times 0.83 \times 10^{-2}} \\ }
\mathrm{ \lambda=9.93 \times 10^{-34+212} \approx 0.01 \AA }
 

Posted by

Ajit Kumar Dubey

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