Test: Dual Nature of Radiation and Matter - 1 - CUET Humanities MCQ

In photoelectric effect for a given photosensitive material, there exists a certain minimum cut-off frequency, called the threshold frequency, below which no emission of photoelectrons takes place, no matter how intense the light is.

Energy will be maximum corresponding to the minimum wavelength.


or
E = 37500 eV
E = 37.5 keV

Specific charge of electrons is independent of gas taken.
Increase in photo intensity increases the number of electrons.

Wavelength of incident radiation is λ = 1100 Å = 1100 x 10^-10m. Therefore, frequency of incident radiation is 

Threshold wavelength is λ₀ = 330 Å = 330 x 10^-10 m. Therefore, threshold frequency is 

Since v < v_n, no photoelectron is emitted.

From Planck's quantum theory, light travels in the form of small bundles or packets of energy called photons. The energy of each photon is
E = hv = 
where h is Planck's constant, v is frequency, c is speed of light and  is wavelength.
Given,  = 6000 , E₁ = 3.32 × 10^-19 J,  = 4000 .
∴ 
⇒ 
⇒ E₂ = × 3.32 × 10^-19 J
= 4.98 × 10^-19 J
=  eV = 3.1 eV

Work function is given by 
Where  is the threshold wavelength.

K.E. of emitted electrons = radiation of energy - work function
= 6.2 eV - 4.2 eV = 2 eV = 2 x 1.6 x 10^-19 J = 3 x 10^-19 J (approx.)

hv = hv_o + E_max
E_max = eV₀, where V₀ is the stopping potential.
Therefore, 

The photoelectric effect is based on the law of conservation of energy.
Energy of the emitted photon = Energy of the incident photon - Work Function