An electron is moving with an initial velocity `vecv=v_0hati` and is in a magnetic field `vecB=B_0hatj`. Then its de-Broglie wavelength

Options

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

Answer

A

Explanation

Given, `vecv = v_0 hati implies vecB = B_0 hatj`
Force on moving electron due to magnetic field is, `F =-e(vecv xxvecB)`
`=-e[v_0 hati xxB_0 hatj] = -eV_0 B_0hatk`
As this force is perpendicular to `vecv` and `vecB` , so the magnitude of `vecv` will not change, i.e., momentum `=(mvecv)` will remain constant in magnitude. Hence, de-Broglie wavelength `lamda = h/(mv)` remains constant.