If E1, E2, and E3 represent respectively the kinetic energies of an electron and an alpha particle and a proton each having same de-broglie wavelength then

Question

If E1, E2, and E3 represent respectively the kinetic energies of an electron and an alpha particle and a proton each having same de-broglie wavelength then (A) E1 > E3 > E2 (B) E2 > E3 > E1 (C) E1 > E2 > E3 (D) E1 = E2 = E3

Tardigrade Admin · Accepted Answer

Since, K.E. = (1/2) mv2 and λ = (h/mv) ∴ K.E. = (1/2) m (h2/m2 λ2) = (h2/2m λ2) As λ is the same. ∴ K.E. propto (1/m)

Q. If $E_{1}, E_{2},$ and $E_{3}$ represent respectively the kinetic energies of an electron and an alpha particle and a proton each having same de-broglie wavelength then

$E_{1} > E_{3} > E_{2}$

$E_{2} > E_{3} > E_{1}$

$E_{1} > E_{2} > E_{3}$

$E_{1} = E_{2} = E_{3}$

Since, $K . E . = \frac{1}{2} m v^{2}$ and $λ = \frac{h}{m v}$
$∴ K . E . = \frac{1}{2} m \frac{h ^{2}}{m ^{2} λ ^{2}} = \frac{h ^{2}}{2 m λ ^{2}}$ As $λ$ is the same.
$∴ K . E . \propto \frac{1}{m}$

Q. If E1​,E2​, and E3​ represent respectively the kinetic energies of an electron and an alpha particle and a proton each having same de-broglie wavelength then

E1​>E3​>E2​

E2​>E3​>E1​

E1​>E2​>E3​

E1​=E2​=E3​