Answer
The de Broglie wavelength remains the same.
Work Step by Step
We can use Equation (38-20) to find an expression for the de Broglie wavelength:
$\frac{1}{2}mv^2 = \frac{h^2}{2m \lambda^2}$
$\lambda^2 = \frac{h^2}{m^2~v^2}$
$\lambda = \frac{h}{m~v}$
Since the electron is moving perpendicular to the magnetic field, there is a magnetic force on the electron that causes the electron to move in a circle. However, the speed does not change.
Therefore, the de Broglie wavelength remains the same.
