Whose Formula should I use?

[ecology665]

Hello Everyone, I am an undergraduate studying - Environmental Science. My question is whose formula do I use? I used mnemonics to learn the Fundamental Constants from a Chemistry book only to find the numbers are different in the other Chemistry textbooks, and Physics textbooks that I have. I found a website 'physics.nist.gov' and they have even different numbers for the constants? I am confused. Should I go ahead and re-learn the numbers the physics website gives? (I don't want to bump head with a professor who governs from the textbook.)

 

I have yet to take Calculus, so I don't understand the numbers in parenthesis for formulas? For example, Electron mass - m_e is 9.109 382 15 (45) x10-31 kg. What does the (45) represent?

 

[timo]

The (45) represents that the last two digits of the number, 15 in this case, are a best estimate but with an uncertainty. The (45) is the uncertainty of these digits. Usually, you could interpret it as there being a 67% probability that the real number (I am omitting units and exponent for simplicity of writing) is within an interval +- 0.00000045 around the given number 9.10938215. The exact meaning can differ, but it always reflects an estimate of how accurate the number is. You usually don't need the exact error estimate. What usually is important is the following: If you need the number of 0.1% of accurancy then you can consider the number as precise. If you need 15 digits of accurancy then you can completely forget about getting a result because you only have ~7 relevant digits. And if you need an accurancy of 7-8 digits then you have to use statistics.

 

For your first question: I am surprised if different sources give really different values. There is two ideas that come to my mind:

1) Maybe they state the same quantities in different units which causes a different number.

2) Perhaps the differences are on the last digits. That may well be, because different groups may measure the same property (and will come to slightly different results), perhaps some books use newer, more precise results than others. It is very rare that you need this accurancy, so for most practical reasons all the different values should be identical. In the rare case that you need an exact number I recommend getting them from sources that specialize on measuring or collecting them, not from textbooks. My first source for the electron mass would be the Particle Data Group (PDG), for example

[Sensei]

If you want to learn constants in memory, remember value in eV (electron Volts):
510998.928 eV

and e=1.602176565*10^-19 C.

and of course c=299,792,458 m/s.

Once you have all these three, you can on demand calculate mass in kilograms:

510998.928 * 1.602176565*10^-19 / 299792458^2 = 9.1093829170743*10^-31 kg

Also remember that mass-energy of electron can be derived from Compton frequency/Compton wavelength and Planck constant.

h=6.62606957*10^-34 J*s

f_C=1.23559*10^20 Hz

 

h*f_C=m_e*c²

 

ps. I don't know what for Environment Science student needs all this stuff to remember. It's rather for quantum physicists, high energy/particle physicists, etc.

For your first question: I am surprised if different sources give really different values. There is two ideas that come to my mind:

 

Or books/sources are from different decades.

See history of speed of light measurement for instance:

https://en.wikipedia.org/wiki/Speed_of_light#History

Currently accepted value is from 1983.

Edited July 11, 2015 by Sensei

[timo]

Books/sources from different decades was supposed to be included in "some books use newer, more precise values" . If you meant something differnt, then I did not understand what you mean.

[John Cuthber]

Why bother to memorise the values?

 

It's much more important to know what they actually mean.

[swansont]

If you want to learn constants in memory, remember value in eV (electron Volts):

510998.928 eV

 

and e=1.602176565*10^-19 C.

 

and of course c=299,792,458 m/s.

Except that as a student you will typically not be worrying about solving problems with more than a couple of significant digits. Meaning that 511 keV, 1.6 x 10^-19C and 3 x 10^8 m/s are sufficient. This is part of a larger issue of understanding significant digits, and learning what rounding-off is proper

 

In a reasonably well-taught class, there will not be emphasis on memorizing constants. You can just look them up.

[ecology665]

I would like to Thank You all (Timo, Sensei, John Cuthber, and Swansont) for your comments they were very helpful. For those of you who wonder why I asked. Yes, the textbooks vary in years of copyright. For example, Physics for Scientists and Engineers by Serway & Jewett (copyright 2014) has atomic mass unit 1.660 538 782 (83) x 10^-27 kg, Physics for Scientists and Engineers by Giancoli (copyright 2000) has amu at 1.6605402 (10) x 10^-27 kg. Chemistry by Reger, Goode & Ball as amu at 1.660 539 x 10^-27 kg. There are variations in most of my textbooks for the constants.

 

Sensei, I just finished precalculus last winterim term. I have a choice of Calculus 101 or physics without calculus. I noticed that the information enclosed either in the inset of the front and back of textbooks along with the appendices is information that you need to know or how to derive at attaining it be it formulas or functions.

 

Timo, Thank You for explaining the uncertainty of the given intervals.

[Sensei]

Why bother to memorise the values?

Aren't chemistry experts memorize names of chemical compounds and their typical reactions with other compounds?

In inorganic chemistry it's thousands+ more to remember than just a few constants.

IMHO it's unavoidable for smart person, who is doing reaction of compounds (especially couple times) to remember result of their reaction.

 

Not to mention shortcuts and full names of chemical elements (118 to remember, 50+ almost required to remember).

(Can you imagine "professional" who is searching net for checking what element is f.e. "Au".. ? I cannot..)

 

I even wrote application-game which is learning whole periodic table. It takes hour (or couple hours) of play to remember entire 118 elements (and 118 shortcuts).

IMHO better to learn children periodic table than meaningless poems in primary school..

 

3 x 10^8 m/s are sufficient.

300,000,000 m/s is sufficient for ordinary layman,

not for somebody studying subject.

Edited July 12, 2015 by Sensei

[StringJunky]

Aren't chemistry experts memorize names of chemical compounds and their typical reactions with other compounds?

In inorganic chemistry it's thousands+ more to remember than just a few constants.

IMHO it's unavoidable for smart person, who is doing reaction of compounds (especially couple times) to remember result of their reaction.

 

Not to mention shortcuts and full names of chemical elements (118 to remember, 50+ almost required to remember).

(Can you imagine "professional" who is searching net for checking what element is f.e. "Au".. ? I cannot..)

 

I even wrote application-game which is learning whole periodic table. It takes hour (or couple hours) of play to remember entire 118 elements (and 118 shortcuts).

IMHO better to learn children periodic table than meaningless poems in primary school..

 

 

300,000,000 m/s is sufficient for ordinary layman,

not for somebody studying subject.

Understanding principles and relationships is more important than learning details that you can just look in a book or on the internet for. The numbers you use the most you will remember by repetitively using them anyway.

[John Cuthber]

Aren't chemistry experts memorize names of chemical compounds and their typical reactions with other compounds?

In inorganic chemistry it's thousands+ more to remember than just a few constants.

IMHO it's unavoidable for smart person, who is doing reaction of compounds (especially couple times) to remember result of their reaction.

 

Not to mention shortcuts and full names of chemical elements (118 to remember, 50+ almost required to remember).

(Can you imagine "professional" who is searching net for checking what element is f.e. "Au".. ? I cannot..)

 

I even wrote application-game which is learning whole periodic table. It takes hour (or couple hours) of play to remember entire 118 elements (and 118 shortcuts).

IMHO better to learn children periodic table than meaningless poems in primary school..

 

 

300,000,000 m/s is sufficient for ordinary layman,

not for somebody studying subject.

The symbol for gold isn't going to change.

I do remember the values of some of the fundamental constants to a few sig. fig, but there's no point to spending time explicitly memorising them. As String Junky points out, you will learn them anyway if you use them much.

But the important thing is to remember what todo with the numbers, not what their values are.

[Sensei]

Understanding principles and relationships is more important than learning details that you can just look in a book or on the internet for.

If there would be nuclear Armageddon, or other disaster, books and Internet won't be available anymore..

What you remember will remain.

Either constant values, and formulas are worth to remember. One doesn't exclude other.

Nobody is here opting for remembering just values, without formulas.

 

The numbers you use the most you will remember by repetitively using them anyway.

That's why it's worth to remember exact value (at the moment, until better measured value is known) since beginning.

I learned all constants during over and over and over recalculations of decay energy of different radioactive isotopes, and energy emitted during fusion.

 

Humans remember plentiful of crap like phone numbers (which is for now 9 digits+), while physical constants are more important.

[swansont]

300,000,000 m/s is sufficient for ordinary layman,

not for somebody studying subject.

 

Unless you've got 4 significant digits or more, it's fine.

[John Cuthber]

If there would be nuclear Armageddon, or other disaster, books and Internet won't be available anymore..

What you remember will remain.

Either constant values, and formulas are worth to remember. One doesn't exclude other.

Nobody is here opting for remembering just values, without formulas.

 

 

That's why it's worth to remember exact value (at the moment, until better measured value is known) since beginning.

I learned all constants during over and over and over recalculations of decay energy of different radioactive isotopes, and energy emitted during fusion.

 

Humans remember plentiful of crap like phone numbers (which is for now 9 digits+), while physical constants are more important.

My 'phone remembers phone numbers for me.

In the event of nuclear Armageddon (which, BTW, the internet was explicitly designed to survive) I guess I will struggle to charge my 'phone. On the other hand, there will be nobody to call and I very much doubt that remembering that C is about 2.997925 E 8 m/s will help in any way at all.

 

My recollection of chemistry might help me purify water without remembering the atomic weight of chlorine (which is slightly variable anyway because the isotope ratio isn't constant).

Knowing that you can get chlorine form salt water and a car battery is more likely to help than knowing the value of Faraday's constant.

Edited July 12, 2015 by John Cuthber