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

Options

A. Remains constant
B. Increases with time
C. Decreases with time
D. Increases and decreases perdiocally.

Answer

A

Explanation

Here,`vecv=v_(0)hati, vecB=B_(0)hatj` Force on moving electron due to magnetic field is `vecF=-e(vecvxxvecB)=-e(v_(0)hatixxB_(0)hatj)=-ev_(0)B_(0)hatk`
As this force is perpendicular to `vecv` and `vecB`, so the magnitude of `vecv` will not change. i.e. momentum `(=mv)` will remain constant in magnitude.Therefore, de Broglie wavelength,`lambda(h/(mv))` remains constant.