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 periodically

Answer

A

Explanation

`vecv = v_0 hati " and " vec B = B_0 hatj` (given)
The electron is moving in a transverse magnetic field. It experience a force `vec F = q(vecV xx vecB) because q=-e`
`therefore vecF = - e (v_0hati xx B_0hatj) = -ev_0B_0hatk [ because hati xx hatj = hatk]`
As this force is perpendicular to `vecv " and " vec B`, the magnitude of `vecv` will remain constant.
`therefore` the momentum mv will also remain constant
`therefore` de broglie wavelength `lamda = (h)/(mv) ` will remain constant