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The property of Caesium that makes it such a stable oscillator is the lone electron in its $6s$ orbital. All other electrons in the lower energy levels take a symmetrical electron configuration and leave the $6s$ as an "outsider". The spin of the Caesium nucleus can cause a so-called hyperfine transition in that $6s$ electron which has a very specific ...
Every atom, including cesium-133, emits (or absorbs) electromagnetic waves (light or its generalization to invisible colors) when the electrons jump from one state in the atom to another. The electromagnetic radiation is a periodic process in which the electric (and similarly magnetic) fields at a given point of space behave as $$E = E_0 \cdot \cos (2\pi f ... 2 Both are correct. It is a matter of personal preference which you decide to use. It makes the graph easier to understand if axes are labelled in small numbers; it also makes the graph less cluttered. So either you would label the x axis "Pressure in units of 10^6 Pa" or "Pressure in MPa". Labelling the x axis as "Pressure in Pa" and using marker values ... -1 The most Natural way where to base units on is to base them on the Planck length and Planck time wich are universal lengths. So you can set the Planck length and Planck time equal to one. They are not based on human measures or alien measures. Every scientific thinking being in the universe would agree on how big these units are. And because all other units ... 0 It is T^{-1}. Consider a rod of length l, marked at l/4, l/2 and 3l/4, and let it rotate with angular velocity \omega about the centre (l/2) point. Now quite clearly the end points are moving twice as fast -- they cover twice the distance per unit time -- as the points marked l/4 and 3l/4, so the dimensions can not be L/T, as the whole ... 0 Your are mistaken. One way of giving the angular velocity is \omega=\frac{|v| \sin{\theta}}{|r|} which gives \frac{\frac{L}{T}}{L}=\frac{1}{T}. We are talking about a change in angle over time, the spatial dimension is given by the r radial distance from the origin without which the angular velocity has no meaning. I always recommend writing all ... 0 Most physics exams would expect you to quote unit for the gradient. However, the axes are labeled as quantity/unit so that the scale is a pure number. (unitless) By this token the gradient should also be a pure number. If you wish to interpret the gradient as being some physical quantity, then you have to " put the units in" ie reverse the process by which ... 0 You can just use equation 3 as a definition. Yes, its dimension will differ from that of momentum, but this is not a big deal. That would not be a worse 4-vector than that of equation 1 - they differ just by a constant factor. And to use equation 2 you use a system of units where c=1, not 1 m/s. 1 I think this question has been asked already several times, for example : How do we know that F = ma, not F = k \cdot ma Are Newton's "laws" of motion laws or definitions of force and mass? Why isn't it E \approx 27.642 \times mc^2? Constants of proportionality depend on the nature of the equation and the system of units. Their ... 2 I think your problem is that you didn't change the units in the constant g. It has a value of approximately 9.8ms^{-2}. Notice that it depends on meters. To obtain the correct result, you should use 980cms^{-2}. Notice that this constant is off by a factor of 100, so that the result (after the square root) is off by a factor of \sqrt{100}=10. 0 Dimensionless is not a dimension, but rather the lack of it. Your made-up rule #1 would not be violated because it applies only to quantities that have dimensions. If you also want to handle quantities that lack dimension, then you will have to know what were the dimensions, before they "cancelled out." For example: if you have a quantity that has l/l ... 0 If you're setting \hbar=1, then you don't - you can't - distinguish between energy and angular frequency. They are, in fact, the same quantity, since E=\hbar\omega=\omega. Similarly, if \hbar=1 you can no longer draw dimensional distinctions between wavevectors and linear momenta, or between angular momenta and pure numbers. In general, you only set ... -1 In the case of energy, I find it more useful to use the reciprocal of time rather than frequency. Time is a much more fundamental (and common) dimension. In other words E=1/T, and of course, T=1/E. 2 When you work "fairly hard", your body can produce about 200 W of power - enough for two incandescent bulbs. Top athletes can produce more - in short bursts. Your body is roughly 25% efficient in converting "calories" (which are actually kilo calories) to Joules - meaning that if you work out hard enough to burn 600 kcal per hour, then you actually produced ... 2 A (kilo)calorie is a unit of energy, while a watt is a unit of power, which describes the rate at which energy is expended. So a 100W bulb is using 100 joules a second. A kcal is about 4184 joules, so a 100W bulb takes about 42 seconds to consume (really: convert into light and heat) a kcal. The joule is the SI (derived) unit of energy. Units of energy ... 4 An average person uses approx. 1500-2500kcal/day. Since one kcal equals 4148J in SI units, that's between 6.2-10.4MJ per day. A day has 86400 seconds, which brings us to an average power consumption of 72-120W... about as much as a light bulb. :-) Physical exercise varies between light (300kcal/h) at an additional 350W to very strenuous at probably six ... 2 The Dimensions of Angle depend on one's viewpoint and purpose (of using dimensions). Likewies the Units (and implicitly scale) of angle also depend on the local customs and practices that support those viewpoints and purposes. Personally, I want Angles to be a dimension, particularly for error detection and correction in scientific and engineering ... 0 (Thanks to Drebin J.) Let's suppose there's a building with many floors, labelled G, 1-10, and after that continues with A1, A2... A10, B1,B2 etc. A1 is floor 1 but actually the 11th, while A2 is 2nd but actually 12th. (Similar to Celsius in Kelvin) Supposing I jump from A2 to A1 (from the staircase), it would obviously hurt. The damage incurred ... 1 In an exam, Alice scored 50, Bob scored 40, Eve scored 10. Now to raise the class mean, the teacher decided to add 20 points to every students. So Alice's score becomes 70, Bob's score becomes 60, and Eve's score becomes 30. Now Alice complained to the teacher, "my score was higher than Bob's by 10 marks, and you see, according to the ... 0 This seems to me like the general "Problem", that differences of Observables behave in a different way, than the observables itself do: One other example (that has nothing to do with additivity or multiplicativity, as you stated) are differences of frequencies: You know that you can convert a frequency to a wavelength by dividing c by the frequency: ... 1 Celsius and Kelvin are two scales that differs only for an additive factor, but the single increment corresponds to the same temperature difference. In other words, an object become "hotter" in the same way if you rise its temperature by 1K or 1°C. You can use conversion formula in differences, just make sure you use it for both terms and keep in mind that ... 0 A temperature change of 1^\circC is the same as a temperature change of 1K. So if you start at 30^\circC (= 303.15K ) and increase the temperature by 5^\circC (5K) the new temperature is 30 + 5 = 35^\circC (303.15 + 5 = 308.15K). 0 temperature difference is 5°C, which is convertible to 278.15K. This is where you go wrong. A difference of 5°C is a difference. Express it as you will in Celcius, Kelvin, Rankine or even in Fahrenheit. But it is a difference. Saying 5°C, which is convertible to 278.15K mean that you are not looking at a difference. Instead you are calculating how to ... 1 No. Beside the already mentioned examples here some real problems with different dimensionless quantities and why they cannot be mixed. :( Starting with angle velocity units: Hertz (Hz) for frequency f measured in periods per seconds (which is equivalent to \frac{2 \cdot \pi}{s}) or Angular frequency \omega measured in \frac{rad}{s} You can ... 1 Of course, you can do it with Matlab, Mupad, Maple, Mathematica or even the Smart Math Calculator. Use this method: First define your variables with your units of choice, then tell the programm what the conversion factors from the given units to the target units are, for example, if you have km/h and need m/sec define 1km as 1000m and 1sec as h as 60² ... 8 Here is an entertaining mathematical answer. (Or at least, I find it entertaining, anyway.) Let us take seriously the idea that we can treat radians as a unit, and proceed from there. This means that when we write an expression like \sin \theta, the argument \theta must have units of radians, whereas the result (I'll assume) is just a number without any ... 0 In your example, a wavelength and a wavenumber represent in a different way the same information as there is a direct conversion between the two quantities. You can use the same reasoning to answer your question about the m/s and s/m: You have a speed v. Let's define a new quantity based on that speed,$$\rho = \frac{1}{v}$$which we conveniently call ... 2 Thing is that the very concept of "dimensions" is unphysical in general, it's a human construct that was invented to allow people to do computations when not being able to compare different quantities for whatever reason (insufficient knowledge, wanting to use incompatible units in the same equation etc.). In reality, everything really is dimensionless, ... 3 I personally think that one should not confuse an angle, say \alpha, and the ratio between \ell the arc length of a circle and its radius r, at least from the outset. As far as fundamental concepts are concerned, angles need a new type of "thing" to be talked about; they are neither a length nor a time interval for example. Moreover, from a ... 1 Think in terms of coordinate transforms as a generalization of unit conversions. When converting between units, you are doing a very simple coordinate transform on the, single, corresponding physical dimension: Multiplication*. When adding two angles, you are really dealing with, for example, a polar coordinate system. The underlying territory ... 1 There are two mistakes. As AccidentalFourierTransform pointed out, the coefficient 7.181\times 10^{-16}, when converted from MeV to eV, should give 7.181\times 10^{-46}. Mega means a million, and it to the fifth power gives 10^{30}, not just 10^{15}. In this way, the OP has to add a 10^{-15} factor to his result. That makes his result 10^{-3} ... 2 From the paper, which states fiber Bragg gratings (FBG) have been demonstrated to exhibit temperature dependent shifts in resonant wavelength of 10 pm/K it is fairly clear that the unit is picometer per kelvin. That is, you have some device with a resonance wavelength \lambda_\mathrm{R} which depends on temperature, ... 8 Think of it this way: is dozen dimensionless? radians (1), degrees (0.017), and gradians (0.0157) are all like dozen (12). Convention says that degree is for angles, and dozen is for eggs. No one goes around saying 562 degrees m/s/s, just like no one says 0.82 dozen m/s/s. They say 9.8 m/s/s. But they totally could. There's no fundamental mathematical or ... 6 I answered another unit based question very much related to this. In it, I pointed out that units are not a fundamental concept in the underpinnings of the universe. They are a concept which people have found helpful for relating the real world to mathematical equations we use to describe the world. Thus, their primary purpose is to be useful. In ... 1 Few of the answers thus far have directly addressed empirical equations, such as the following: Vapor pressure of isobutane (source)$$ \log_{10}{P_\mathrm{mmHg}}=6.74808-{882.80\over 240.0+T_\mathrm{^\circ C}} $$Seeton model for kinematic viscosity of various liquids (source; K_0 is the zero-order modified Bessel function of the second kind)$$ ...