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A proton is projected in a uniform magnetic field of induction B in a direction perpendicular to the field. Mass of proton is m, charge is e. If radius of its trajectory is r, what is the de Broglie wavelength of the proton? Given $B = 1 T, r = 1 m, m = 1.67 x 10^{- 27} kg$

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$4.45 x 10^{- 15} m$

$8.23 x 10^{- 12} m$

$6.14 x 10^{- 14} m$

$12.34 x 10^{- 6} m$

answer is A.

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Detailed Solution

The trajectory is a circle

Angular velocity $ω$ = eB/m

$∴ λ = \frac{h}{p} = \frac{h}{eBr} = \frac{6.625 x 10^{- 34}}{1.6 x 10^{- 19} x 1 x 1} m = 4.14 x 10^{- 15} m$

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