# Mass of electron

1. Mar 16, 2012

### johann1301

When i look up the mass of an electron, wikepedia says: 9.10938291(40)×10−31 kg

Fine, but what does the (40) stand for? Is there 40 more or total decimals, or is there uncertainty in weather the 40 belongs there or not?

or some other reason maybe??

:)

2. Mar 16, 2012

### Khashishi

9.10938291(40)×10−31 kg means 9.10938291×10−31 kg +- 0.00000040×10−31 kg
Numbers in parentheses are experimental uncertainty in the last given digits.

3. Mar 16, 2012

### johann1301

Thanks;)

4. Mar 18, 2012

### dazza95

It means that 9.10938291 have all been confirmed the right values, and its a prediction that the next 2 numbers are 4 and 0
Thanks,
Z.c

5. Dec 29, 2012

### Anti-Crackpot

I realize this topic is a bit dated, but still worth a quick follow-up...
Well... no, actually. As Khashishi noted, the 4 and 0 relate to standard uncertainty and are associated with the last two digits 9, 1, meaning that the value for electron mass is probably 9.10938291*10^-31 kg, plus or minus .00000040 * 10^-31. Easy to see if you go to the NIST site and check out the value for electron mass: http://physics.nist.gov/cgi-bin/cuu/Value?me

Furthermore, the mass of an electron is a dependent constant. It is not measured directly, but takes it's value from formulas such as the following: 2Rh/c*alpha^2 where R is the Rydberg constant, h is Planck's constant, c is the speed of light, and alpha is the fine structure constant. R has been measured to a high degree of precision, c is fixed by definition, h is increasingly being measured to a high degree of precision, leaving alpha, a constant the measurement of which you can read about on Wikipedia. See: http://en.wikipedia.org/wiki/Fine-structure_constant#Measurement. If any of the above values change, then so too does the value for electron mass.

Not sure how the standard uncertainty is calculated, but it's in some manner a combination of the standard uncertainty associated with R, h and alpha.

So, for example, numerically, using CODATA 2010 values, and without reference to units: (2Rh)/(c*alpha^2) = (2*1.0973731568539*10^7*6.62606957*10^(-34))/(299792458*137.035999074^(-2)) = 9.10938290*10^-31, which is off on the last digit, but that's almost certainly a rounding error.

- AC

Last edited: Dec 29, 2012