KE MAX
= HV – O
To prove the
equation of photoelectrons, we'll start with the fundamental principles of the
photoelectric effect.
1. Photon
Energy:
The energy E Photon of an
incoming photon is
Ephoton= hv
where h is Planck's constant and v is the
frequency of the photon.
2. Work
Function:
The work function o of a material is
the minimum energy required to eject an electron from the surface of the
material.
3. Photoelectric
Effect:
When a photon strikes the material, its
energy is transferred to an electron. To eject an electron, the photon must
provide at least as much energy as the work function. Any additional energy
beyond this threshold is converted into the kinetic energy of the emitted
electron.
4. Conservation
of Energy:
According to the conservation of energy, the
total energy of the photon is used to overcome the work function and to impart
kinetic energy to the electron. Therefore:
E photon = o +E kin
Here, E kin is the kinetic energy of the emitted electron.
5. Maximum
Kinetic Energy:
The maximum kinetic energy K.E max
of the emitted electron occurs when the photon energy is just enough to
overcome the work function, leaving the maximum possible energy for the
electron's kinetic energy. Rearranging the energy conservation equation to
solve for K.E MAX
E kin = E PHOTON – O
Substituting
EPhoton HV ,
KE MAX
= HV – O
This
equation, KE MAX = HV – O , shows that the maximum kinetic
energy of the emitted photoelectron is the difference between the energy of the
incident photon and the work function of the material.
Links:
1. Photoelectric effects and its significance
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