First slide

Matter waves (DC Broglie waves)

Question

The ratio of de-Broglie wavelength of a α-particle to that of a proton being subjected to the same magnetic field so that the radii of their path are equal to each other assuming the field induction vector $\vec{B}$ is perpendicular to the velocity vectors of the α-particle and the proton ts

Difficult

A

1
B

1/4
C

1/2
D

2

Solution

When a charged particle (charge q, mass m) enters perpendicularly in a magnetic field (B) than, radius of the path described by it
$\begin{array}{l} r = \frac{mv}{qB} \Rightarrow mv = qBr . \\ Also de - Broglie wavelength λ = \frac{h}{mv} \Rightarrow λ = \frac{h}{qBr} \Rightarrow \frac{λ_{α}}{λ_{p}} = \frac{q_{p} r_{p}}{q_{α} r_{α}} = \frac{1}{2} \end{array}$

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