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If E1,E2 and E3 represent respectively the kinetic energies of an electron, 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
Correct answer is option 'A'. Can you explain this answer?
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If E1,E2 and E3 represent respectively the kinetic energies of an elec...
According to de broglie, 
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If E1,E2 and E3 represent respectively the kinetic energies of an elec...
Explanation:

De Broglie Wavelength Formula:
- The de Broglie wavelength (λ) of a particle is given by the formula: λ = h/p, where h is the Planck's constant and p is the momentum of the particle.

Given Information:
- E1, E2, and E3 represent the kinetic energies of an electron, an alpha particle, and a proton, respectively, with the same de Broglie wavelength.

Relationship between Kinetic Energy and Momentum:
- The kinetic energy of a particle is related to its momentum by the equation: K.E. = p^2 / 2m, where p is the momentum and m is the mass of the particle.

Analysis:
- Since all the particles have the same de Broglie wavelength, they have the same momentum.
- Considering the formula for kinetic energy in terms of momentum, the kinetic energy is inversely proportional to the mass of the particle.

Explanation of Option 'A' (E1 > E3 > E2):
- Electron (E1) has the least mass among the three particles, so it will have the highest kinetic energy.
- Proton (E3) has more mass compared to the alpha particle (E2), so it will have lower kinetic energy than the electron but higher than the alpha particle.
- Alpha particle (E2) has the highest mass among the three particles, resulting in the lowest kinetic energy.
Therefore, the correct order of kinetic energies for particles with the same de Broglie wavelength is E1 > E3 > E2, which corresponds to option 'A'.
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If E1,E2 and E3 represent respectively the kinetic energies of an electron, 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 = E3Correct answer is option 'A'. Can you explain this answer?
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