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An electron is moving with an initial ve...

An electron is moving with an initial velocity `vecv=v_(0)hati` and is in a magnetic field `vecB=B_(0)hatj`
Then it's de-Broglie wavelength

A

remains constant

B

Increases with time.

C

decreases with time

D

increases and decreases periodically

Text Solution

Verified by Experts

The correct Answer is:
A
Magnetic force acting on electron,
`vecF_(m)=(vecBxxvecv)`
`=e{B_(0)hatjxxv_(0)hati}`
`=eB_(0)v_(0)(hatjxxhati=eB_(0)v_(0) (-hatk))`
`implies` Direction of `vecF_(m)` would be along-Z axis which is perpendicular to `vecv`.Hence,given electron would perform circular motion with constant speed `v_(0)` in a plane perpendicular to magnetic field.Hence ,its de-Broglie wavelength would be constant equal to `lambda=(h)/(mv_(0))` .In above eqution h,m ,`v_(0)` are same hence wavelength `lambda` will remian constant.
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