If the momentum of an electron is changed by P , then the de-Broglie wavelength associated with it changes by 0.5 % . The initial momentum of electron will be,

Question

If the momentum of an electron is changed by P , then the de-Broglie wavelength associated with it changes by 0.5 % . The initial momentum of electron will be, (A) 200P (B) 400P (C) (P/200) (D) 100P

Tardigrade Admin · Accepted Answer

The de-Broglie wavelength associated with an electron is, λ =(h/P) , or, P=(h/λ ) , ∴ (Δ P/P)=-(Δ λ /λ ) ⇒ (P/P textinitial)=(0 . 5/100) Therefore, P textintial=200P

Q. If the momentum of an electron is changed by $P$ , then the de-Broglie wavelength associated with it changes by $0.5%$ . The initial momentum of electron will be,

$200 P$

$400 P$

$\frac{P}{200}$

$100 P$

The de-Broglie wavelength associated with an electron is,
$λ = \frac{h}{P}$ ,
or, $P = \frac{h}{λ}$ ,
$∴ \frac{Δ P}{P} = - \frac{Δ λ}{λ}$
$\Rightarrow \frac{P}{P _{initial}} = \frac{0.5}{100}$
Therefore,
$P_{intial} = 200 P$

Q. If the momentum of an electron is changed by P , then the de-Broglie wavelength associated with it changes by 0.5% . The initial momentum of electron will be,

200P

400P

200P​

100P