A proton and an α-particle are accelerated from rest to the same energy. The de Broglie wavelengths λp and λα are in the ratio,

Question

A proton and an α-particle are accelerated from rest to the same energy. The de Broglie wavelengths λp and λα are in the ratio, (A) 2: 1 (B) 1: 1 (C) √ 2 :1 (D) 4: 1

Tardigrade Admin · Accepted Answer

λ = (h/√2mEk) (∵ Ek is same for both) ⇒ (λp/λα) = √(4m/m) = 2: 1

Q. A proton and an $α$ -particle are accelerated from rest to the same energy. The de Broglie wavelengths $λ_{p}$ and $λ_{α}$ are in the ratio,

2 : 1

1 : 1

$2$ :1

4 : 1

$λ = \frac{h}{2 m E _{k}} (∵ E_{k}$ is same for both)
$\Rightarrow \frac{λ _{p}}{λ _{α}} = \frac{4 m}{m}$
$= 2 : 1$

Q. A proton and an α-particle are accelerated from rest to the same energy. The de Broglie wavelengths λp​ and λα​ are in the ratio,