An electron, an alpha particle and a proton have the same kinetic energy. Which one of these particles has (i) the shortest and (ii) the largest, de Broglie wavelength?

Question

Verified by Toppr

Answer 1

De Broglie wavelength of particle of mass m in terms of kinetic energy $(E_{k})$ is $λ = \frac{h}{2 m E _{k}} \propto \frac{1}{m}$ for the same kinetic energy.
(i) Out of given particles, the mass of alpha particle is maximum, so de Broglie wavelength associated with alpha particle is the shortest.
(ii) As mass of electron is least, so electron has largest de-Broglie wavelength.

Answer 2

De Broglie wavelength of particle of mass m in terms of kinetic energy

(E_{k})

is

λ = \frac{h}{2 m E _{k}} \propto \frac{1}{m}

for the same kinetic energy.
(i) Out of given particles, the mass of alpha particle is maximum, so de Broglie wavelength associated with alpha particle is the shortest.
(ii) As mass of electron is least, so electron has largest de-Broglie wavelength.

An electron, an alpha particle and a proton have the same kinetic energy. Which one of these particles has (i) the shortest and (ii) the largest, de Broglie wavelength?

An electron, an alpha $(α)$ particle and a proton have same kinetic energies. Which one of these particles has largest de Broglie wavelength?

An electron, an $α$ particle and a proton have the same kinetic energy. Which of these particles has the shortest de Broglie wavelength?

If $E_{1}, E_{2}, E_{3}$ are the respective kinetic energies of an electron, an $α$ -particle and a proton, each having the same de-Broglie wavelength, then

An electron and a proton have the same kinetic energy. Which one of the two has the larger de Broglie wavelength and why?

If the particles listed below all have the same kinetic energy, which one would posses the shortest de-Broglie wavelength.

Revise with Concepts

Wave Nature of Matter

Wave Nature of Matter - Problem L1

An electron, an alpha particle and a proton have the same kinetic energy. Which one of these particles has (i) the shortest and (ii) the largest, de Broglie wavelength?

An electron, an alpha (α) particle and a proton have same kinetic energies. Which one of these particles has largest de Broglie wavelength?

An electron, an α particle and a proton have the same kinetic energy. Which of these particles has the shortest de Broglie wavelength?

If E1​,E2​,E3​ are the respective kinetic energies of an electron, an α-particle and a proton, each having the same de-Broglie wavelength, then

An electron and a proton have the same kinetic energy. Which one of the two has the larger de Broglie wavelength and why?

If the particles listed below all have the same kinetic energy, which one would posses the shortest de-Broglie wavelength.

Revise with Concepts

Wave Nature of Matter

Wave Nature of Matter - Problem L1

An electron, an alpha $(α)$ particle and a proton have same kinetic energies. Which one of these particles has largest de Broglie wavelength?

An electron, an $α$ particle and a proton have the same kinetic energy. Which of these particles has the shortest de Broglie wavelength?

If $E_{1}, E_{2}, E_{3}$ are the respective kinetic energies of an electron, an $α$ -particle and a proton, each having the same de-Broglie wavelength, then