De Broglie Hypothesis

Circumference =

According to de-Broglie hypothesis

De-Broglie wavelength is given by
,
where is the ground state energy of the hydrogen atom
whose value is

The de-Broglie wavelength is related to the momentum of a particle by the equation: where is the de-Broglie wavelength, is Planck's constant, and is the momentum of the particle. For a photon, the momentum is related to its energy by the equation: where is the energy of the photon and is the speed of light. For an electron, the momentum is given by: where is the de-Broglie wavelength of the electron. Since the electron and photon are given to have the same de-Broglie wavelength, their momentum must also be the same. - Velocity: The velocities of the electron and photon are not necessarily the same, since their masses are different (photon has no rest mass while the electron does). - Momentum: The electron and photon have the same de-Broglie wavelength, hence the same momentum. - Angular momentum: Angular momentum depends on the specific motion of the particle and is not directly related to the de-Broglie wavelength. - Energy: The energy of the photon and electron are not necessarily the same, as their energies depend on different factors (photon's energy depends on frequency, electron's energy depends on its kinetic energy). Thus, the correct answer is momentum.