An α -particle moves in a circular path of radius 0.83 cm in the… | NEET 2012 (AIPMT, Prelims)

Q143NEET 2012 · AIPMT · PRELIMSMedium

Matter Waves: de Broglie Wavelength

An $\alpha$ -particle moves in a circular path of radius 0.83 cm in the presence of a magnetic field of 0.25 Wb/m2. The de Broglie wavelength associated with the particle will be

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Answer: (d)

Circular motion: $r = \dfrac{mv}{qB} \Rightarrow p = qBr$ , so $\lambda = \dfrac{h}{qBr}$ .
$q = 2e = 3.2\times10^{-19}$ C, $qBr = 3.2\times10^{-19}\times0.25\times0.83\times10^{-2} = 6.64\times10^{-22}$
$\lambda = \dfrac{6.63\times10^{-34}}{6.64\times10^{-22}} \approx 10^{-12}$ m $= 0.01$ Å
So the answer is (d) 0.01 Å.

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