The de-Broglie wavelength of a particle accelerated with 150 volt potential is 10-10 m. If it is accelerated by 600 volts p.d., its wavelength will be

Question

The de-Broglie wavelength of a particle accelerated with 150 volt potential is 10-10 m. If it is accelerated by 600 volts p.d., its wavelength will be (A) 0.25 mathringA (B) 0.5 mathringA (C) 1.5 mathringA (D) 2 mathringA

Tardigrade Admin · Accepted Answer

By using λ propto (1/√V) ⇒ (λ1/λ2)=√(V2/V1) ⇒ (10-10/λ2)=√(600/150)=2 ⇒ λ2=0.5 mathringA

Q. The de-Broglie wavelength of a particle accelerated with $150$ volt potential is $1 0^{- 10} m$ . If it is accelerated by $600$ volts p.d., its wavelength will be

$0.25 \overset{˚}{A}$

$0.5 \overset{˚}{A}$

$1.5 \overset{˚}{A}$

$2 \overset{˚}{A}$

By using $λ \propto \frac{1}{V}$
$\Rightarrow \frac{λ _{1}}{λ _{2}} = \frac{V _{2}}{V _{1}}$
$\Rightarrow \frac{1 0 ^{- 10}}{λ _{2}} = \frac{600}{150} = 2$
$\Rightarrow λ_{2} = 0.5 \overset{˚}{A}$

Q. The de-Broglie wavelength of a particle accelerated with 150 volt potential is 10−10m. If it is accelerated by 600 volts p.d., its wavelength will be

0.25A˚

0.5A˚

1.5A˚

2A˚