The ratio of wavelengths of proton and deuteron accelerated through the same potential difference will be

Question

The ratio of wavelengths of proton and deuteron accelerated through the same potential difference will be (A) 1: 2 (B) 2: 1 (C) √2: 1 (D) 1: √2

Tardigrade Admin · Accepted Answer

λ=(h/√2 q V m) Since both proton and deuteron have same charge and accelerated through the same potential difference. λ propto (1/√m) ∴ (λp/λd)=√(md/mp) =√(2 mp/mp)=√2

Q. The ratio of wavelengths of proton and deuteron accelerated through the same potential difference will be

$1 : 2$

$2 : 1$

$2 : 1$

$1 : 2$

$λ = \frac{h}{2 q Vm}$
Since both proton and deuteron have same charge and accelerated through the same potential difference.
$λ \propto \frac{1}{m}$
$∴ \frac{λ _{p}}{λ _{d}} = \frac{m _{d}}{m _{p}}$
$= \frac{2 m _{p}}{m _{p}} = 2$

Q. The ratio of wavelengths of proton and deuteron accelerated through the same potential difference will be

1:2

2:1

2​:1

1:2​

λ=2qVm​h​ Since both proton and deuteron have same charge and accelerated through the same potential difference. λ∝m​1​ ∴λd​λp​​=mp​md​​​ =mp​2mp​​​=2​

$1 : 2$

$2 : 1$

$2 : 1$

$1 : 2$

$λ = \frac{h}{2 q Vm}$
Since both proton and deuteron have same charge and accelerated through the same potential difference.
$λ \propto \frac{1}{m}$
$∴ \frac{λ _{p}}{λ _{d}} = \frac{m _{d}}{m _{p}}$
$= \frac{2 m _{p}}{m _{p}} = 2$