Planck Units. - The Planck units are a set of natural units derived from fundamental constants:

·         Name                                  Dimension     Value (SI units)
·         Planck length(ℓᴘ)                length (L)        1.616255(18) ×10⁻³⁵ m.
·          Planck mass                      mass (M)        2.176434(24) ×10⁻⁸ kg.
·         Planck time                       time (T)          5.391247(60) ×10⁻⁴⁴ s.
·         Planck temperature            temperature (Θ)1.416784(16) ×10³² K.
·         Planck angular frequency (ωᴘ)rad/s           1.885 × 10⁴³ s⁻¹
·         Planck’s frequency (fᴘ):      Hz                 2.952 ×10⁴² Hz
·         Planck Constant (h)                                6.62607015 × 10⁻³⁴ J·s 
·       The energy of Planck Frequency is              E ≈ 1.232×10⁹ J            

The Planck frequency, a repeating event that occurs once every Planck period (Fp) with a frequency of about 2.952 ×10⁴² Hz. This frequency is called the upper limit of frequency of electromagnetic waves or cosmic rays.

The Planck units are a set of natural units derived from fundamental constants, such as the speed of light, Planck's constant, and the gravitational constant. These units represent the scale at which quantum effects become significant and are used in theoretical physics to explore phenomena at the smallest scales or in extreme conditions.

The Planck frequency is not directly obtained as the inverse of the Planck time (5.391247×10^-44 s). Instead, it's derived from fundamental physical constants such as Planck's constant (h), the speed of light (c), and the gravitational constant (G), utilizing these values in the formula for frequency.

The precise value for the Planck frequency is approximately 2.952 ×10⁴² Hz, calculated from these constants and their relationships, and it's considered a fundamental limit in physics, just like other Planck units. This frequency is not directly the inverse of the Planck time but is a distinct value derived from different fundamental constants and their interrelations.

The Planck frequency (Fp) is a frequency that corresponds to the inverse of the Planck time. It is approximately 2.952 ×10⁴² Hz. This frequency represents an upper limit for the frequency of electromagnetic waves or cosmic rays.

The Planck length (L) (ℓP) is approximately 1.616255(18)×10^−35 meters. It is considered the smallest meaningful length scale in the universe.

The Planck mass (M) is approximately 2.176434(24)×10^−8 kilograms. It represents the mass at which quantum gravitational effects become important.

The Planck time (T) (tP) is approximately 5.391247(60)×10^−44 seconds. It is the smallest meaningful unit of time and represents the time it takes for light to travel the Planck length.

The Planck temperature (Θ) is approximately 1.416784(16)×10^32 Kelvin. It is the highest temperature that can be meaningfully defined in physics.

It's worth noting that there may be slight variations in the reported values of Planck units due to ongoing research and refinement of measurement techniques.

These Planck units provide a theoretical framework for understanding the fundamental scales of the universe, but their extreme values make them inaccessible to current experimental observations. They are primarily used in the context of theoretical physics and as a basis for exploring quantum gravity and the nature of spacetime at the Planck scale."

Additional:

Planck units are a set of units of measurement defined exclusively in terms of four universal physical constants. Originally proposed by the German physicist Max Planck in 1899, these units are a system of natural units because their definition is based on properties of nature. It may be mentioned here that Einstein first published his special theory of relativity in 1905, which describes his revolutionary ideas about light, time and energy.

The four universal constants, by definition, have a numerical value of 1 when expressed in these units:

1. Speed of light in vacuum, c,

2. Gravitational constant, G,

3. Reduced Planck constant, ħ, and

4. Boltzmann constant, kB.

• Planck length = ℓP = L ≈ 1.61626 × 10^−35 m; 

• Planck time = tP = T ≈ 5.391247 × 10^−44 s; 

• ℓP/tP is the ratio of the Planck length to the Planck time;

Since, ℓP/tP = (1.61626 × 10^−35 m) / (5.391247 × 10^−44 s);

1. To divide two numbers in scientific notation, we subtract the exponents of the 10 and divide the coefficients:

2. Coefficient: (1.61626) / (5.391247) ≈ 0.299792458

3. Exponent: (10^(-35)) / (10^(-44)) = 10^(-35 - (-44)) = 10^9

4. So the simplified value is approximately:

5. 0.299792458 × 10^9 m/s

6. Now, we recognize that this is the speed of light in a vacuum, which is denoted by 'c':

7. c ≈ 2.99792458 × 10^8 m/s

8. So, the simplified expression is:

9. (1.61626 × 10^−35 m) / (5.391247 × 10^−44 s) ≈ 2.99792458 × 10^8 m/s;

The ratio of the Planck length to the Planck time (ℓP/tP) yields a value to the speed of light in a vacuum, c;

This is a fundamental constant in physics and is denoted by 'c'.

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