Why is the basic charge not equal to the reciprocal of a Coulomb?

[snowjoe]

why isn't the number of e or p making a Coulomb the same as the reciprocal of the 'basic' charge if the basic charge is defined as a fraction of a Coulomb?

basic charge = 1.6 x e-19C, but number of p or e constituting a C is 6.25 x e18

 

[Orodruin]

Yes? 1/1.6e-19 = 6.25e18

 

[snowjoe]

Yes? 1/1.6e-19 = 6.25e18

thank you. i may be getting stupid, but why isn't the number of e or p 1.6 e19, if each e or p, basic charge, has a charge

Yes? 1/1.6e-19 = 6.25e18

there's something I'm not getting. if a quantity x was 1/10th of y, it would take 10 x's to make y. why not 1.6 e19 e or p to make 1 C?

 

[Orodruin]

thank you. i may be getting stupid, but why isn't the number of e or p 1.6 e19, if each e or p, basic charge, has a charge

Because 1/1.6 is not equal to 1.6. Imagine instead that 1 C was the charge of 20 = 2e1 protons. This would make the basic charge 1/20 = 0.05 = 5e-2 C. Obviously, this is not equal to 2e-1, which it would be if you applied the same logic as the one you just applied.

there's something I'm not getting. if a quantity x was 1/10th of y, it would take 10 x's to make y. why not 1.6 e19 e or p to make 1 C?

Because 10*1/10 = 1 while 1.6e19 * 1.6e-19 = 1.6^2, which is not equal to one.

 

[Drakkith]

there's something I'm not getting. if a quantity x was 1/10th of y, it would take 10 x's to make y. why not 1.6 e19 e or p to make 1 C?

If quantity X is 0.2 of Y, then 1/0.2 = 5, meaning it takes 5X to equal Y. If X is 15 millionths of Y, then 1/0.000015 = 66,666, so it takes 66,666 X to equal Y.

 

[snowjoe]

If quantity X is 0.2 of Y, then 1/0.2 = 5, meaning it takes 5X to equal Y. If X is 15 millionths of Y, then 1/0.000015 = 66,666, so it takes 66,666 X to equal Y.

still, .2 is 1/5. and 5x = y so if a quantity is 1/ 15 millionth of another it would take 15 million of that quantity to equal that other, as it requires 5 of the amount that is 1/5 (.2) of another to equal that other amount

 

[Drakkith]

so if a quantity is 1/ 15 millionth of another it would take 15 million of that quantity to equal that other

No it doesn't. I just showed you the math in my post.

 

[snowjoe]

i know, the math makes sense, but i can't see my way around the logical demand that a fractional part of a quantity is that fraction because it takes the amount denominated to equal the whole quantity. the example of .2 follows this logic, five .2s equal the whole, .2 is the fraction 1/5

 

[SteamKing]

i know, the math makes sense, but i can't see my way around the logical demand that a fractional part of a quantity is that fraction because it takes the amount denominated to equal the whole quantity.

I have no idea what you mean here.

the example of .2 follows this logic, five .2s equal the whole, .2 is the fraction 1/5

That's because 0.2 = (2/10) = (1/5) in its simplest terms, and 5 * (1/5) = 1.

However,
1 / 1.6 = 1 / (16 / 10) = (10 / 16) = 5 / 8 = 0.625

 

[Drakkith]

i know, the math makes sense, but i can't see my way around the logical demand that a fractional part of a quantity is that fraction because it takes the amount denominated to equal the whole quantity. the example of .2 follows this logic, five .2s equal the whole, .2 is the fraction 1/5

Yes, but look at your original numbers.
basic charge (c)= 1.6 x 10^-19C
C = 6.25 x 10¹⁸c

1.6 x 10^-19 is already a fraction equal to 1/6.25x10¹⁸, just like 0.2 is a fraction equal to 1/5. You multiply 0.2 times 5 to get 1, and you multiply 1.6x10^-19 by 6.25x10¹⁸ to get 1.

there's something I'm not getting. if a quantity x was 1/10th of y, it would take 10 x's to make y. why not 1.6 e19 e or p to make 1 C?

If you're getting confused over the fact that 1.6x10^-19 is not 1/1.6x10¹⁹, then the only way I know of understanding this is to just do the math.
1.6x10^-19 = 1/X
1.6x10^-19X = 1
X = 1/1.6x10^-19
X = 6.25 x 10¹⁸

Similarly: 0.2 = 1/X
0.2X = 1
X = 1/0.2
X = 5

 

[andrevdh]

Let's say it takes N electrons to make up one coulomb of charge then

N x e = 1 C

so

N = 1 coulomb / 1.6 x 10^-19 coulomb

Historycally the coulomb, a certain amount of charge or electrons, was defined
via the ampere - the amount of current in 2 parallel wires 1 meter apart in a vacuum
when the magnetic force on one meter of these wires is 2 x 10^-7 Newton.

 

[A.T.]

i know, the math makes sense, but i can't see my way around the logical demand...

Is math not logical enough?

 

[Orodruin]

Let's say it takes N electrons to make up one coulomb of charge then

N x e = 1 C

so

N = 1 coulomb / 1.6 x 10^-19 coulomb

Historycally the coulomb, a certain amount of charge or electrons, was defined
via the ampere - the amount of current in 2 parallel wires 1 meter apart in a vacuum
when the magnetic force on one meter of these wires is 2 x 10^-7 Newton.

I do not think this is where the OP's confusion lies, but rather in the fact that the reciprocal of 1.6e-19 is not 1.6e19, see post #4.

 

[andrevdh]

Yes, that is why I started to mention the definition of the ampere.
Maybe that might clear it up.

 

[snowjoe]

Yes, but look at your original numbers.
basic charge (c)= 1.6 x 10^-19C
C = 6.25 x 10¹⁸c

1.6 x 10^-19 is already a fraction equal to 1/6.25x10¹⁸, just like 0.2 is a fraction equal to 1/5. You multiply 0.2 times 5 to get 1, and you multiply 1.6x10^-19 by 6.25x10¹⁸ to get 1.
If you're getting confused over the fact that 1.6x10^-19 is not 1/1.6x10¹⁹, then the only way I know of understanding this is to just do the math.
1.6x10^-19 = 1/X
1.6x10^-19X = 1
X = 1/1.6x10^-19
X = 6.25 x 10¹⁸

Similarly: 0.2 = 1/X
0.2X = 1
X = 1/0.2
X = 5

Thanks, you explained this beautifully

 

[snowjoe]

Is math not logical enough?

yeh, math, logical, mind, not so much, sometimes

 

[andrevdh]

The mind is much like a muscle.
The more you use it the stronger it gets.