In a photoelectric effect experiment a light of frequency 1.5 times the threshold frequency is made to fall on the surface of photosensitive material. Now if the frequency is halved and intensity is doubled, the number of photo electrons emitted will be:

We need to determine what happens to photoelectron emission when frequency is halved and intensity is doubled.

Key Concept: Photoelectric Effect

Photoelectrons are emitted only when the frequency of incident light is greater than or equal to the threshold frequency ($$\nu_0$$). This is Einstein's photoelectric equation:

$$KE_{max} = h\nu - h\nu_0$$

Initial condition: Frequency = $$1.5\nu_0 > \nu_0$$ (above threshold, photoelectrons are emitted).

New condition: Frequency halved = $$\frac{1.5\nu_0}{2} = 0.75\nu_0$$.

Since $$0.75\nu_0 < \nu_0$$ (below threshold frequency), no photoelectrons will be emitted, regardless of the intensity. Increasing intensity only increases the number of photons, but each photon still has energy $$h \times 0.75\nu_0 < h\nu_0$$, which is insufficient to eject an electron.

The correct answer is Option 3: Zero.