Electromagnetic Waves and Spectrum

The electromagnetic spectrum order by increasing frequency: radio waves (lowest frequency), visible light, ultraviolet, X-rays (highest frequency). This matches option C: 4,1,3,2. Frequency is inversely proportional to wavelength, and energy increases with frequency.

Sound wave is the odd one out because it is a mechanical wave that requires a medium (solid, liquid, or gas) to propagate. In contrast, X-rays, gamma rays, and microwaves are all electromagnetic waves that can travel through vacuum and do not require any medium for propagation.

1 terahertz (THz) equals 10^12 hertz. 1 kilohertz (kHz) equals 10^3 hertz. Therefore, 1 THz = 10^12 Hz = 10^12 / 10^3 kHz = 10^9 kHz = 1,000,000,000 kHz. Option A correctly shows this conversion. Options B, C have incorrect digit counts, and D has an extra zero.

In the electromagnetic spectrum, visible light ranges from about 400-700 nanometers. Ultraviolet has shorter wavelengths (<400nm), while infrared has longer wavelengths (>700nm). X-rays have extremely short wavelengths, and thermal radiation is a broad category not specific to solar spectrum position.

A light year is a unit of distance, not time or speed. It represents the distance light travels in one vacuum year (about 9.46 trillion kilometers). Astronomers use it to measure vast interstellar and intergalactic distances.

X-rays have wavelengths typically in the range of 0.1 to 10 angstroms (10^-11 to 10^-10 meters), making 1 angstrom the correct order of magnitude. Micron (10^-6 m) is for infrared, centimeter and meter scales are for radio/microwave regions.

The visible light spectrum ranges from approximately 3900 to 7600 angstroms (390-760 nanometers), covering violet through red. Options A (8500-9800) and B (7800-8000) are in the infrared range, while D (1300-3000) is in the ultraviolet range.

A light year is a unit of distance representing the distance light travels in one vacuum year (about 9.461 trillion km). It measures vast astronomical distances, not energy, speed, or intensity.

Red light occupies the longest wavelength region of the visible spectrum, approximately 610-760 nanometers. This range represents the lower energy end of visible light, with wavelengths longer than orange (590-610nm) and shorter than infrared (beyond 760nm).

The beam-width of Hertizian dipole is 180^o and its half power beam-width is 90^o.

Using $\Delta f$ =$\dfrac{c \Delta \lambda}{\lambda^2}$, where $\Delta \lambda$ = 2 x 10^-7 And      $\lambda$ = 10^-6 $\Delta f$ = 60,000 GHz

Noise power is same for both which is $\dfrac{N_0}{2}$

Thus probability of error will be lower for the constellation 1 as it has higher signal energy.

By using solution we get                        Energy of constellation 1 = 14 a^2                      Energy of constellation 2 = 4 a^2                                                  Ratio = 14 a^2/4 a^2 = 3.5