An α particle and a proton are accelerated from rest by a potential difference of 200 V. After this, their de Broglie wavelengths are λα and λ p respectively. The ratio (λ p /λa) is

Question

An α particle and a proton are accelerated from rest by a potential difference of 200 V. After this, their de Broglie wavelengths are λα and λ p respectively. The ratio (λ p /λa) is (A) 3.8 (B) 8 (C) 7.8 (D) 2.8

Tardigrade Admin · Accepted Answer

λ=( h / p )=( h /√2 m q V ) (λ p /λα)=√( m α q α/ m p q p )=√(4 m p × 2 e / m p × e )=√8=2 √2 =2 √2 (λ p /λα)=2 × 1.4=2.8

Q. An $α$ particle and a proton are accelerated from rest by a potential difference of $200 V$ . After this, their de Broglie wavelengths are $λ_{α}$ and $λ_{p}$ respectively. The ratio $\frac{λ _{p}}{λ _{a}}$ is

3.8

8

7.8

2.8

$λ = \frac{h}{p} = \frac{h}{2 m q V}$
$\frac{λ _{p}}{λ _{α}} = \frac{m _{α} q _{α}}{m _{p} q _{p}} = \frac{4 m _{p} \times 2 e}{m _{p} \times e} = 8 = 22$
$= 22$
$\frac{λ _{p}}{λ _{α}} = 2 \times 1.4 = 2.8$

Q. An α particle and a proton are accelerated from rest by a potential difference of 200V. After this, their de Broglie wavelengths are λα​ and λp​ respectively. The ratio λa​λp​​ is

3.8

8

7.8

2.8

λ=ph​=2mqV​h​ λα​λp​​=mp​qp​mα​qα​​​=mp​×e4mp​×2e​​=8​=22​ =22​ λα​λp​​=2×1.4=2.8

Q. An $α$ particle and a proton are accelerated from rest by a potential difference of $200 V$ . After this, their de Broglie wavelengths are $λ_{α}$ and $λ_{p}$ respectively. The ratio $\frac{λ _{p}}{λ _{a}}$ is

$λ = \frac{h}{p} = \frac{h}{2 m q V}$
$\frac{λ _{p}}{λ _{α}} = \frac{m _{α} q _{α}}{m _{p} q _{p}} = \frac{4 m _{p} \times 2 e}{m _{p} \times e} = 8 = 22$
$= 22$
$\frac{λ _{p}}{λ _{α}} = 2 \times 1.4 = 2.8$