Q.

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=1T, r=1m, m=1.67 x 10-27 kg

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a

8.23x 10-12m

b

12.34 x 10-6m

c

4.45 x 10-15m

d

6.14 x 10-14m

answer is A.

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Detailed Solution

The trajectory is a circle

Angular velocity ω = eB/m

λ=hp=heBr=6.625 x 10-341.6 x 10-19x 1 x1 m=4.14 x 10-15 m

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