Question

A moving proton and electron have the same deBroglie wavelength. If $K$ and $P$ denote the $K . E$. and momentum respectively. Then choose the correct option:

• A. $K _{ p }< K _{ e }$ and $P _{ p }= P _{ e }$
• B. $K _{ p }= K _{ e }$ and $P _{ p }= P _{ e }$
• C. $K _{ p }< K _{ e }$ and $P _{ p }< P _{ e }$
• D. $K _{ p }> K _{ e }$ and $P _{ p }= P _{ e }$

Answer 1

Answer: (A)

$\lambda_{P}=\frac{h}{P_{P}} $
$\lambda_{e}=\frac{h}{P_{e}}$
$\because \lambda_{ P }=\lambda_{ e }$
$\Rightarrow P _{ P }= P _{ e }$
$( K )_{ P }=\frac{ P _{ P }^{2}}{2 m _{ P }}$
$( K )_{ e }=\frac{ P _{ e }^{2}}{2 m _{ e }}$
$K _{ P }< K _{ e }$ as $m _{ P }> m _{ e }$