To understand the correct answer, let's start by understanding the concept of the threshold wavelength in photoelectric emission.

1. Photoelectric Effect:
The photoelectric effect refers to the emission of electrons from a metal surface when it is illuminated with light. This phenomenon can be explained by considering light as a stream of particles called photons. When photons interact with the metal surface, they transfer their energy to the electrons, causing them to be emitted.

2. Threshold Wavelength:
The threshold wavelength is the minimum wavelength of light required to cause photoelectric emission from a metal surface. It is determined by the energy required to overcome the binding energy of the electrons in the metal. If the wavelength of light is longer than the threshold wavelength, it does not possess enough energy to liberate electrons.

3. Relationship between Energy and Wavelength:
The energy of a photon is directly proportional to its frequency (E = hf), where h is the Planck's constant and f is the frequency. Additionally, the frequency of light is inversely proportional to its wavelength (f = c/λ), where c is the speed of light and λ is the wavelength. Combining these equations, we get E = hc/λ.

Explanation of the correct answer:

From the given options, we need to choose the lamp that emits light with a wavelength shorter than the threshold wavelength of 5200 Å.

a) 1 W IR lamp: Infrared (IR) light has longer wavelengths than visible light, so it will have a wavelength greater than 5200 Å. Therefore, photoelectrons will not be emitted from the metal surface when illuminated with this lamp.

b) 50 W UV lamp: Ultraviolet (UV) light has shorter wavelengths than visible light, so it will have a wavelength shorter than 5200 Å. Therefore, photoelectrons will be emitted from the metal surface when illuminated with this lamp.

c) 50 W IR lamp: As mentioned earlier, IR light has longer wavelengths than visible light, so it will have a wavelength greater than 5200 Å. Therefore, photoelectrons will not be emitted from the metal surface when illuminated with this lamp.

d) 10 W IR lamp: Similar to option (c), the IR light emitted by this lamp will have a wavelength greater than 5200 Å. Therefore, photoelectrons will not be emitted from the metal surface when illuminated with this lamp.

Hence, the correct answer is option (b) - 50 W UV lamp, as it emits light with a wavelength shorter than the threshold wavelength of 5200 Å.