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:

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

Tardigrade Admin · Accepted Answer

λP=(h/PP) λe=(h/Pe) ∵ λ P =λ e ⇒ P P = P e ( K ) P =( P P 2/2 m P ) ( K ) e =( P e 2/2 m e ) K P < K e as m P > m e

Q. 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:

$K_{p} < K_{e}$ and $P_{p} = P_{e}$

$K_{p} = K_{e}$ and $P_{p} = P_{e}$

$K_{p} < K_{e}$ and $P_{p} < P_{e}$

$K_{p} > K_{e}$ and $P_{p} = P_{e}$

$λ_{P} = \frac{h}{P _{P}}$
$λ_{e} = \frac{h}{P _{e}}$
$∵ λ_{P} = λ_{e}$
$\Rightarrow P_{P} = P_{e}$
$(K)_{P} = \frac{P _{P}^{2}}{2 m _{P}}$
$(K)_{e} = \frac{P _{e}^{2}}{2 m _{e}}$
$K_{P} < K_{e}$ as $m_{P} > m_{e}$

Q. 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:

Kp​<Ke​ and Pp​=Pe​

Kp​=Ke​ and Pp​=Pe​

Kp​<Ke​ and Pp​<Pe​

Kp​>Ke​ and Pp​=Pe​