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When a piece of metal is illuminated by a monochromatic light of frequency ν, then stopping potential is Vs. When same surface is illuminated by light of frequency 2ν, then stopping potential becomes 3Vs. The value of threshold frequency for photoelectric emission will be

When a piece of metal is illuminated by a monochromatic light of frequency ν, then stopping potential is Vs. When same surface is illuminated by light of frequency 2ν, then stopping potential becomes 3Vs. The value of threshold frequency for photoelectric emission will be Correct Answer <span class="math-tex">\(\frac{\nu}{2}\)</span>

CONCEPT:

Additional Information

​Laws of Photoelectric Effect:

  1. For a light of any given frequency; (f > fTh) photoelectric current is directly proportional to the intensity of light
  2. For any given material, there is a certain minimum frequency, called threshold frequency, below which the emission of photoelectrons stops completely, no matter how high is the intensity of incident light.
  3. The maximum kinetic energy of the photoelectrons is found to increase with the increase in the frequency of incident light, provided the frequency (f > fTh) exceeds the threshold limit. The maximum kinetic energy is independent of the intensity of light.
  4. The photoelectric emission is an instantaneous process without any apparent time lag (10-9 sec or less), even when the intensity of the incident radiation is made extremely low.​
  5. The intensity of radiation is proportional to the number of energy quanta per unit area per unit time. The greater the number of energy quanta available, the greater is the number of electrons absorbing the energy quanta and greater is the number of electrons coming out of the metal.
  • Stopping potential: It is defined as the potential required to stop the ejection of an electron from a metal surface when the incident beam of energy is greater than the work function of the metal.
  • Work function: It is the minimum amount of energy required so that metal emits an electron. It is represented by ϕ.
  • If Vo is the stopping potential then Einstien's photoelectric equation can be written as,

⇒ eVo = hν - ϕo

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একটি ধাতব তলে λ তরঙ্গদৈর্ঘ্যের একবর্ণী আলোকরশ্মি আপতিত হলে ফটো-ইলেক্ট্রন নির্গত হয় এবং এক্ষেত্রে বিভবের মান 3Vo একই তলে যখন 2λতরঙ্গদৈর্ঘ্যের একবর্ণী আলো আপতিত হয়, তখন নিবৃত্তি বিভবের মান Vol ফটো-ইলেক্ট্রন নির্গত হওয়ার জন্য ঐ তলটির সূচন তরঙ্গদৈর্ঘ্যের মান নির্ণয় কর।(A monochromatic light of wavelength λ is incident on a metallic surface then ejects photo-electron and the value of stopping potential is 3Vo. When the same surface is illuminated by a light of wavelength 2λ., the stopping potential becomes Vo. Calculate the threshold wavelength for this surface to eject photo electrons.)
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