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Zorluk: ZorPhotoelectric Effect and Work Function

Monochromatic light of frequency 9.0×1014 Hz9.0 \times 10^{14}\text{ Hz} is incident on a clean potassium emitter surface having a threshold frequency of 5.0×1014 Hz5.0 \times 10^{14}\text{ Hz}. Given that Planck's constant h=6.6×10−34 J⋅sh = 6.6 \times 10^{-34}\text{ J}\cdot\text{s} and the elementary charge e=1.6×10−19 Ce = 1.6 \times 10^{-19}\text{ C}, what is the stopping potential in volts required to completely arrest the photoelectric current?

Cevap: 1.65 V

Cevap

The stopping potential required to arrest the emitted photoelectrons is 1.65 V1.65\text{ V}.
Applying Einstein's photoelectric equation Kmax⁡=hf−hf0=h(f−f0)K_{\max} = h f - h f_0 = h(f - f_0) gives a maximum kinetic energy of 2.64×10−19 J2.64 \times 10^{-19}\text{ J}. Dividing this by the electronic charge e=1.6×10−19 Ce = 1.6 \times 10^{-19}\text{ C} yields the stopping potential Vs=1.65 VV_s = 1.65\text{ V}.

Adım Adım Çözüm

1
Determine the net energy available for photoelectron kinetic energy using Einstein's photoelectric equation
Kmax⁡=h(f−f0)=6.6×10−34 J⋅s×(9.0×1014−5.0×1014) Hz=2.64×10−19 JK_{\max} = h(f - f_0) = 6.6 \times 10^{-34}\text{ J}\cdot\text{s} \times (9.0 \times 10^{14} - 5.0 \times 10^{14})\text{ Hz} = 2.64 \times 10^{-19}\text{ J}
Photoelectron emission occurs only when photon energy hfhf exceeds the work function W0=hf0W_0 = h f_0, with the excess energy appearing as maximum kinetic energy.
2
Express stopping potential in terms of electron charge and maximum kinetic energy
Vs=Kmax⁡e=2.64×10−19 J1.6×10−19 C=1.65 VV_s = \frac{K_{\max}}{e} = \frac{2.64 \times 10^{-19}\text{ J}}{1.6 \times 10^{-19}\text{ C}} = 1.65\text{ V}
The stopping potential VsV_s does work eVse V_s equal to the maximum kinetic energy Kmax⁡K_{\max} of the fastest photoelectrons to bring them to rest.

Anahtar Kavram

Einstein's Photoelectric Equation and Stopping Potential Relationship
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