The de Broglie wavelength λ associated with a proton increases by 25 %, if its momentum is decreased by p0. The initial momentum was

Question

The de Broglie wavelength λ associated with a proton increases by 25 %, if its momentum is decreased by p0. The initial momentum was (A) 4 p0 (B) (p0/4) (C) 5 p0 (D) (p0/5)

Tardigrade Admin · Accepted Answer

(λ2-λ1/λ1)=(25/100) (λ2/λ1)=(5/4) ⇒ (P1/P2)=(5/4) P2-P1=-P0 (4 P1/5)-P1=-P0 P1=5 P0

Q. The de Broglie wavelength $λ$ associated with a proton increases by $25%$ , if its momentum is decreased by $p_{0}$ . The initial momentum was

$4 p_{0}$

$\frac{p _{0}}{4}$

$5 p_{0}$

$\frac{p _{0}}{5}$

$\frac{λ _{2} - λ _{1}}{λ _{1}} = \frac{25}{100}$
$\frac{λ _{2}}{λ _{1}} = \frac{5}{4}$
$\Rightarrow \frac{P _{1}}{P _{2}} = \frac{5}{4}$
$P_{2} - P_{1} = - P_{0}$
$\frac{4 P _{1}}{5} - P_{1} = - P_{0}$
$P_{1} = 5 P_{0}$

Q. The de Broglie wavelength λ associated with a proton increases by 25%, if its momentum is decreased by p0​. The initial momentum was

4p0​

4p0​​

5p0​

5p0​​