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Zorluk: KolayPhotoelectric Effect and Work Function

A metal surface inside a vacuum cell is illuminated by incident photons each having an energy of 6.2 eV6.2\text{ eV}. If the maximum kinetic energy of the emitted photoelectrons is 2.4 eV2.4\text{ eV}, what is the work function of the metal in electron-volts (eV\text{eV})?

Cevap: 3.8 eV

Cevap

The work function of the metal is 3.8 eV3.8\text{ eV}.
According to Einstein's photoelectric equation, the total energy of an incident photon (E=6.2 eVE = 6.2\text{ eV}) equals the work function of the metal (W0W_0) plus the maximum kinetic energy of the ejected photoelectrons (Kmax⁡=2.4 eVK_{\max} = 2.4\text{ eV}). Subtracting the kinetic energy from the photon energy gives W0=6.2 eV−2.4 eV=3.8 eVW_0 = 6.2\text{ eV} - 2.4\text{ eV} = 3.8\text{ eV}.

Adım Adım Çözüm

1
State Einstein's photoelectric equation
E=W0+Kmax⁡E = W_0 + K_{\max}
Relates the incident photon energy to the metal work function and photoelectron kinetic energy.
2
Rearrange the equation to solve for the work function
W0=E−Kmax⁡W_0 = E - K_{\max}
Isolates the work function W0W_0 on one side of the equation.
3
Substitute the given numerical values and compute
W0=6.2 eV−2.4 eV=3.8 eVW_0 = 6.2\text{ eV} - 2.4\text{ eV} = 3.8\text{ eV}
Evaluates the difference to obtain the minimum energy needed to remove an electron.

Anahtar Kavram

Einstein's Photoelectric Equation and Work Function
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Konular

Photoelectric Effect and Work Function

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