CBSE Class 12 · 2015 · Delhi · Modern PhysicsShort Answer

A proton and an

α

-particle have the same de-Broglie wavelength. Determine the ratio of
(i) their accelerating potentials,
(ii) their speeds.

Answer: $V_{p} : V_{α} = 8 : 1$ ; $v_{p} : v_{α} = 4 : 1$ .

Solution

(i)

λ = \frac{h}{2 m q V}

. Equal

λ

gives

m_{p} q_{p} V_{p} = m_{α} q_{α} V_{α}

.
With

m_{α} = 4 m_{p}

and

q_{α} = 2 q_{p}

\frac{V _{p}}{V _{α}} = \frac{m _{α} q _{α}}{m _{p} q _{p}} = 4 \times 2 = 8 \Rightarrow V_{p} : V_{α} = 8 : 1.

(ii)

λ = \frac{h}{m v}

. Equal

λ

gives

m_{p} v_{p} = m_{α} v_{α}

\frac{v _{p}}{v _{α}} = \frac{m _{α}}{m _{p}} = 4 \Rightarrow v_{p} : v_{α} = 4 : 1.

V_{p} : V_{α} = 8 : 1, v_{p} : v_{α} = 4 : 1

CBSE Class 12 Board · 2015 · Delhi · Subjective