Question

The threshold frequency for a metal is \[8 \times {10^1}^4hertz\]. What is the kinetic energy of the electron having frequency \[{10^{15}}{s^{ - 1}}\]?

Answer 1

Hint: We know that in the photoelectric effect, light exhibits its particle quality, implying that light is made up of photons. When light strikes a metal surface, each electron on the surface can only absorb one photon at a time. The energy of a photon is determined by its frequency. As long as the photon's frequency is higher than the threshold frequency, one electron that absorbs it will have enough energy to overcome the pull of other electrons, allowing it to be released.

Complete answer:
For this question, we will be using Einstein's equation of kinetic energy.
It is given by \[\dfrac{1}{2}{m_e}{v^2}\].
We have Kinetic energy\[ = \dfrac{1}{2}{m_e}{v^2}\]
\[ = h(\nu - {\nu _o})\]
(here, h= Plank constant, \[{\text{\nu }}\]= frequency, \[{{\text{\nu }}_{\text{o}}}\]= threshold frequency
Substituting the values, we get,
\[{\text{K}}{\text{.E}}{\text{. = (6}}{\text{.626}} \times {\text{1}}{{\text{0}}^{34}}Js) \times (1.0 \times {10^{15}}{s^{ - 1}} - 8.0 \times {10^{14}}{s^{ - 1}})\]
\[ = {\text{(6}}{\text{.626}} \times {\text{1}}{{\text{0}}^{34}}Js) \times (10.0 \times {10^{14}}{s^{ - 1}} - 8.0 \times {10^{14}}{s^{ - 1}})\]
\[ = {\text{(6}}{\text{.626}} \times {\text{1}}{{\text{0}}^{34}}Js) \times (2.0 \times {10^{14}}{s^{ - 1}})\]
\[ = 1.3252 \times {10^{ - 19}}\]
Thus, the kinetic energy of the electron is \[1.3252 \times {10^{ - 19}}\]\[J\].

Additional information:
Because light is bundled into photons, Einstein theorised that when a photon collides with a metal's surface, the entire photon's energy is transferred to the electron. A portion of this energy is used to free the electron from the metal atom's grasp, while the rest is given to the ejected electron as kinetic energy.

Note:
It must be noted that the photoelectric effect occurs when light of suitable frequency is incident on a metal surface, causing electrons to be emitted. Heinrich Hertz first described the photoelectric effect in 1887, and Lenard followed suit in 1902. However, neither of the photoelectric effect's discoveries could be explained by Maxwell's electromagnetic wave theory of light. Einstein then used the idea that light was a particle.