In which one of the following regions of electromagnetic spectrum, LASER is most difficult to achieve?

The difficulty in achieving laser action increases with the frequency of the radiation. This is primarily due to the relationship between spontaneous emission and stimulated emission. The Einstein A coefficient, which represents the rate of spontaneous emission, is proportional to the cube of the frequency (ν³).

In the Ultraviolet (UV) region, frequencies are significantly higher than in the microwave, infrared, or visible regions. Because the spontaneous emission rate is so high at these frequencies, the excited atoms return to the ground state almost instantly. This makes it extremely difficult to maintain the population inversion necessary for laser action, requiring an immense amount of pumping power compared to lower-frequency regions.

Historically, the first MASER (Microwave) was easier to achieve than the optical laser, and UV/X-ray lasers remain the most technically challenging due to these fundamental physical constraints.