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Physics constant, also referred to as the fundamental constant or the universal constant, is a physical quantity that is generally believed to be universal in nature and has a constant value in time. It is unlike a mathematical constant, which has a fixed numerical value, however, does not directly involve any physical measurement.
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Constant Value in Physics
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In physics, we generally have to deal with various dimensions. In order to set these dimensions of an entity, the time length of an event, or the density of the fluid, they are required to be compared with other entities, we use as a reference. These entities are referred to as the constants of physics, such as the speed of light (c), the charge of the electron(e) or mass (mp) of a proton, Rydberg constant, and so on. For example, the value of Avogadro's number is 6.02214 x 10²³ mol?¹ remains the same everywhere.
Famous Constants in Physics
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Famous Constants in Physics are provided below:
| S.No. | Name | Symbol | Value |
|---|---|---|---|
| 1. | Speed of light in the vacuum | c | 3 x 108 m/s |
| 2. | Planck’s constant | h | 6.62607015 x 10-34J. s |
| 3. | Gravitational constant | G | 6.673 x 10-¹¹ Nm²/kg² |
| 4. | Elementary charge | e, qe (charge of a proton) | 1.602176634 x 10-19 C |
| 5. | Electric constant | ε0 | 8.9875517923(14) x 109 kg.m³. s-4.A-2 |
| 6. | Alpha particle mass | mα | 6.644657230(82) x10-27 kg 4.001506179127(63) u 3.727379378(23) GeV/c² |
| 7. | Deuteron mass | mD | 2.013553212745(40) u 1875.612928(12) MeV 1.67377 x 10-27kg or 1.67377 x 10-24g |
| 8. | Proton mass | mp | 1.672621898(21) x 10-27kg 1.672621898(21) x 10-24 kg 1.007276466879(91)u 938.2720813(58) MeV/c² |
| 9. | Neutron mass | mn | 1.674927471(21) x 10-27 kg 1.674927471(21) x 10-24 1.00866491588(49) u 939.5654133(58) MeV/c² |
| 10. | Electron mass | me | 9.10938356(11) x 10-³¹ kg 9.10938356(11) x 10-28g 5.48579909070(16) amu 0.5109989461(31) MeV/c² |
| 12. | Boltzmann’s constant | Kb | 1.380649 x 10-23 J/K 1.380649 x 10-16erg/K |
| 13. | Gas constant | R | 8.3144598(48) J/K mol 8.3144598(48) x 10³ amu.m²/s²K 8.3144598(48) x 10-2 L.bar/K mol 8.3144598(48) m³ .Pa/K.mol 62.363577(36) L.T or/K.mol 1.9872036(11) x 10-3Kcal/K.mol 8.2057338(47)x10-5m³.atm/K.mol 0.082057338(47) L.atm/K.mol |
Important Physics Constants
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Important Physics Constants are:
| S.No. | Name | Formula | Value |
|---|---|---|---|
| 1. | Von Klitzing constant | Rk = 2πh/e² | 25812.80745...Ω |
| 2. | Curie constant | C = X (T - \(\theta \)) | 1.3047 K * A/ (T * m) |
| 3. | Fine-structure constant | α = e²/2hcε0 | 0.007297351 |
| 4. | Compton wavelength | λ = h/mc | In meter: 2.42 x 10-¹²m In Angstrom = 0.242 Å |
| 5. | Impedance of free space | Z0 = 1/ε0c0 | 376.730...Ω |
| 6. | Bohr radius | a0 = 4πε0 h²/e²me | 0.0529 m |
| 7. | Faraday constant | F = eNA | 96,485 C/mol |
| 8. | Vacuum electric permittivity | ε0 = 1/μ0c² | 8.854 x 10-¹² F.m |
| 9. | Stefan–Boltzmann constant | σ = π²k4/60h³c² | 5.67 x 10-8Js-¹m-²K-4 |
| 10. | Thomson cross section | σe = (8π/3) re² | 6.6524587321 x 10-29 m² |
| 11. | Vacuum magnetic permeability | μ0 | 1.25663706212(19)x10-6N. A-² |
| 12. | Reduced Planck constant | h = h/2π | 1.05457 x 10-34J. s |
| 13. | Josephson constant | KJ = 2e/h | 483597.84... x 108Hz. /V |
| 14. | Rest mass of the electron | me = 2R∞h/cα2 | 0.51099895000(15) Mev |
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Nature of Physics Constants
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The fundamental constants, based on nature can be categorized into-
- A: Characteristic of a particular system – Characteristic of light)
- B: Characteristic of a class of physical phenomena – Characteristic of electromagnetic phenomena
- C: Universal Constants – Discovered after the discovery of special relativity
There are some Physics constants that can take the dimensional form like – speed of light; unlike the other few that are dimensionless like- fine structure constant. Some physics constants are material constants, meaning they possess constant value for a material. A constant can use multiple equivalent units like – SI, natural units, atomic mass units, CGS units, etc. Some physics constants are redefined by fixing the SI values. But this certainly increases the uncertainty in the value of physics constants.
Fundamental Constants in Physics
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Here are the fundamental constants in Physics-
- Speed of light in vacuum = c
- Planck’s constant = h
- The electric constant = ε0
- The elementary charge = e
Things To Remember
- Physical constants, also known as fundamental or universal constants, are generally universal and are physical quantities that are expected to have constant values over time.
- The fundamental constants, based on nature can be categorized into 3 categories- Characteristic of a particular system, Characteristic of a class of physical phenomena, and Universal Constants.
- To set these dimensions of an entity, the time length of an event, or the density of the fluid, they are required to be compared with other entities with reference.
- The fundamental constants in Physics- Speed of light in vacuum = c, Planck’s constant = h, The electric constant = ε0, The elementary charge = e.
Important PYQs Related To This Chapter
- What is dimensional formula of thermal conductivity… (DUET 2006)
- In the formula X=3YZ2, X and Z have dimensions…
- The frequency of vibration of string is given by… (BHU UET 2004)
- Dimensions of surface tension… (BHU UET 2001)
- The radius of sphere is measured to be… (JCECE 2005)
- A gas bubble formed from an explosion under water… (JCECE 2007)
- If E= energy, G= gravitational constant, I= impulse… (BCECE 2008)
- Which of the following is the smallest unit … (UPSEE 2010)
- A quantity z, to be estimated has a dependency on the variables… (TS EMCET 2019)
- If the magnetic flux is represented in weber...(GUJCET 2016)
- Write dimensional formula for the intensity of radiation… (GUJ CET 2007)
- What is the dimensional formula for universal gravitational constant … (COMEDK UGET 2014)
- 'Raman frequencies' refers to...(COMEDK UGET 2008)
- Einstein was awarded Nobel prize for his work in…(COMEDK UGET 2014)
- A body weighs 22.42 g and has a measured volume of...(WBJEE 2010)
Sample Questions and Solved Examples
Ques. What do you understand by the term ‘Physics Constants’? What are the main seven constants? (Mark 3)
Ans. The term ‘Physical constants’, also known as fundamental or universal constants, are generally universal and are physical quantities that are expected to have constant values over time.
Here are the 7 main Physics Constants-
- the cesium hyperfine frequency ΔνCs
- the speed of light in vacuum c
- the Planck constant h
- the elementary charge e
- the Boltzmann constant k
- the Avogadro constant NA, and
- the luminous efficacy of a defined visible radiation Kcd
Ques. What are the Universal Constants? (2 Marks)
Ans. There are four Universal Constants, they are-
- Planck's constant (h),
- The elementary charge (e),
- Boltzmann's constant (k); and
- Avagadro's number, NA (Metrologia, doi: 10.1088/1681-7575/aa950a).
Ques. How to find the Plack’s Constant? (3 Marks)
Ans. We know that, λ=350 Vs=1.45
and, λ=400 Vs=1
350h=w+1.45 (equation 1)
400h=w+1.........(equation 2)
Hence, h = 4.2 x 10-15\(\frac{eV}{s}\)
Ques. An airplane accelerates down a runway at 3.20 m/s2 for 32.8 s until is finally lifts off the ground. Determine the distance traveled before takeoff. (3 Marks)
Ans. d = vi*t + 0.5*a*t2
d = (0 m/s)*(32.8 s)+ 0.5*(3.20 m/s2)*(32.8 s)2
d = 1720 m
Ques. A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine the acceleration of the car and the distance traveled. (3 Marks)
Ans. a = (Delta v)/t
a = (46.1 m/s - 18.5 m/s)/(2.47 s)
a = 11.2 m/s2
d = vi*t + 0.5*a*t2
d = (18.5 m/s)*(2.47 s)+ 0.5*(11.2 m/s2)*(2.47 s)2
d = 45.7 m + 34.1 m
d = 79.8 m
(Note: the d can also be calculated using the equation vf2 = vi2 + 2*a*d)
Ques. A bike accelerates uniformly from rest to a speed of 7.10 m/s over a distance of 35.4 m. Determine the acceleration of the bike. (3 Marks)
Ans. vf2 = vi2 + 2*a*d
(7.10 m/s)2 = (0 m/s)2 + 2*(a)*(35.4 m)
50.4 m2/s2 = (0 m/s)2 + (70.8 m)*a
(50.4 m2/s2)/(70.8 m) = a
a = 0.712 m/s2
Ques. Find the cut off wavelength in a waveguide of two parallel walls 1.5cm apart. Where is E=0 and where is E=maximum? (2 Marks)
Ans. We know that the cut off wavelength λc = 2a =2×1.5 =3cm
Taking E=0 walls as half of the wavelength points that occurs at wall and E= maximum at the middle of that particular wall as \(\frac{λ}{4}\)planes can be couted for.
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