A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of λ. An alpha particle having certain kinetic energy has the same de-Brogle wavelength λ. The ratio of kinetic energy of proton and that of alpha particle is:

Question

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of λ. An alpha particle having certain kinetic energy has the same de-Brogle wavelength λ. The ratio of kinetic energy of proton and that of alpha particle is: (A) 2: 1 (B) 4: 1 (C) 1: 4 (D) 1: 2

Tardigrade Admin · Accepted Answer

K E=(p2/2 m)=(h2/2 m λ2) (K Ep/K Eα)=(mα/mp)=4: 1

Q. A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of $λ$ . An alpha particle having certain kinetic energy has the same de-Brogle wavelength $λ$ . The ratio of kinetic energy of proton and that of alpha particle is:

$2 : 1$

$4 : 1$

$1 : 4$

$1 : 2$

$K E = \frac{p ^{2}}{2 m} = \frac{h ^{2}}{2 m λ ^{2}}$
$\frac{K E _{p}}{K E _{α}} = \frac{m _{α}}{m _{p}} = 4 : 1$

Q. A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of λ. An alpha particle having certain kinetic energy has the same de-Brogle wavelength λ. The ratio of kinetic energy of proton and that of alpha particle is:

2:1

4:1

1:4

1:2