Electromagnetic radiations with wavelengths 200 nm, 500 nm and 1000 nm are given. Which of these wavelengths can produce a visual sensation (visible light) in the human eye?

Introduction / Context:
The electromagnetic spectrum covers a wide range of wavelengths, from very short gamma rays to very long radio waves. The human eye can detect only a narrow band of this spectrum, known as visible light, and radiations outside this band are invisible to us even though they carry energy. This question asks you to determine which of the given wavelengths lie within the visible region and therefore cause visual sensation.

Given Data / Assumptions:

• Three wavelengths are given: 200 nm, 500 nm and 1000 nm.
• The human eye is sensitive to the visible range of approximately 400 nm to 700 nm.
• Wavelengths shorter than about 400 nm are ultraviolet (UV).
• Wavelengths longer than about 700 nm are infrared (IR).

Concept / Approach:
To solve this, we simply compare each of the given wavelengths with the standard visible range. If a wavelength falls within about 400 nm to 700 nm, it will stimulate the retina and be perceived as light of a particular colour. Wavelengths outside that band will not be seen, even though they may have physical effects such as heating or chemical action. We do not need complicated formulas; only a clear understanding of the approximate visible window.

Step-by-Step Solution:
Step 1: Recall that visible light spans roughly from 400 nm (violet) to 700 nm (red). Step 2: Compare 200 nm with this range: 200 nm is less than 400 nm, so it lies in the ultraviolet region and is invisible. Step 3: Compare 500 nm with this range: 500 nm lies between 400 nm and 700 nm, so it is visible, typically perceived as greenish light. Step 4: Compare 1000 nm with this range: 1000 nm is greater than 700 nm, so it lies in the infrared region and is invisible. Step 5: Conclude that only 500 nm is within the visible band and can cause visual sensation.

Verification / Alternative check:
Spectral charts used in physics and biology consistently mark the approximate visible range at 400 to 700 nm, with violet at the short wavelength end and red at the long wavelength end. Ultraviolet radiation, starting below 400 nm, is known for causing sunburn and fluorescence but is invisible. Infrared radiation, starting above about 700 nm, is associated with heat. The given wavelengths of 200 nm and 1000 nm clearly fall into these invisible regions, reinforcing that 500 nm is the only visible wavelength among the options.

Why Other Options Are Wrong:
200 nm and 500 nm: Includes 200 nm, which is ultraviolet and does not produce a visual sensation in the eye.

500 nm and 1000 nm: Includes 1000 nm, which is infrared and invisible, so this pair is not correct.

200 nm and 1000 nm: Both wavelengths are outside the visible range, so neither produces a visual sensation.

Common Pitfalls:
Students sometimes memorise only one end of the visible range and misclassify wavelengths near the boundaries. Others may confuse frequency and wavelength, forgetting that smaller wavelength means higher frequency. A simple way to remember is to associate visible light roughly with 0.4 to 0.7 micrometres (400 to 700 nm). Anything much smaller is UV; anything much larger is IR. Using that rule of thumb quickly identifies 500 nm as visible and the other two as non visible.

Final Answer:
Among the given wavelengths, 500 nm only lies in the visible range and can produce a visual sensation in the human eye.