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## Photoelectric effect

When light of suitable frequency strikes upon a metal surface electrons are emitted from the surface. This phenomenon is called photoelectric effect.

Concepts

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When light of suitable frequency strikes upon a metal surface electrons are emitted from the surface. This phenomenon is called photoelectric effect.

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Einstein's photoelectric equation :

$K_{max}=λhc −φ=hν−φ$

The kinetic energy of the photoelectron coming out may be anything between zero and $(E−φ)$ where $E=λhc $ is the energy supplied to the individual electrons.

$K_{max}=E−φ$

$K_{max}=λhc −φ=hν−φ$

The kinetic energy of the photoelectron coming out may be anything between zero and $(E−φ)$ where $E=λhc $ is the energy supplied to the individual electrons.

$K_{max}=E−φ$

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Photoelectric current is zero when the stopping potential is sufficient to repel even the most energetic photoelectrons with the maximum kinetic energy $K_{max}$ so that $K_{max}=eV_{0}$

For a given frequency of the incident radiation, the stopping potential is independent of its intensity.

For a given frequency of the incident radiation, the stopping potential is independent of its intensity.

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The smallest magnitude of the anode potential which just stops the photocurrent is called the stopping potential.

This potential should stop even the ost energitic photoelectron. Hence

Tha value of maximum kinetic energy should be equal to $eV_{0}$

We know $K_{m}ax=hν−ϕ=λhc −ϕ$

$V_{0}=λehc −eϕ $

This potential should stop even the ost energitic photoelectron. Hence

Tha value of maximum kinetic energy should be equal to $eV_{0}$

We know $K_{m}ax=hν−ϕ=λhc −ϕ$

$V_{0}=λehc −eϕ $

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We know the relation of stopping potential $V_{0}$ with frequency $ν$ is

$V_{0}=eh ν−eW $

where $W$ is the work function of the metal.

If we want to plot the stopping potential $V_{0}$ vs frequency $ν$, it will be a straight line with slope $eh $ and negative y intercept $eW $

$V_{0}=eh ν−eW $

where $W$ is the work function of the metal.

If we want to plot the stopping potential $V_{0}$ vs frequency $ν$, it will be a straight line with slope $eh $ and negative y intercept $eW $

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De Broglie's wavelength is the wavelength associated with a massive particle,hypothesized by De Broglie that explains Bohr's quantised orbits by bringing in the wave-particle duality. It is written as

$λ=mvh $ (de broglie wavelength)

$λ=mvh $ (de broglie wavelength)

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Davison and Germer observed the diffraction of electrons by crystals. The setup consists of an electron gun firing electron beam onto a nickel target inside a vaccum chamber. The diffracted electrons are observed by the galvanometer.The experiment was performed by varying the voltage from 44V to 68V. It was observed that a strong peak appeared when the voltage was 54V at a scattering angle of $50_{0}$ due to constructive interference effects of the electrons. The wavelength of the matter waves was found to be 0.168 nm from diffraction measurements which matches that of de-Broglie wavelength at 54 V thus verifying the wave nature of electrons.