Which constants to use in Saha Equation

  • Thread starter leroyjenkens
  • Start date
  • Tags
    Constants
In summary, the equation has an exponential term with units that need to cancel, but the second term with the 3/2 exponent gives an incorrect result for units. However, by rearranging the equation and including the k in the numerator, everything else in the equation can be cancelled and the final answer is in meters cubed.
  • #1
leroyjenkens
616
49
I'll post a picture of the equation and a picture of the problem I'm being asked. My problem is I can't get the units to cancel. This is a ratio, so the final answer is supposed to be unitless. The exponential term obviously needs the units to cancel, so I chose the correct Boltzmann constant for the units to cancel in that one, so I think I'm good there. The first term with the Pe in the denominator always gives me meters cubed as the units. So if I can get inverse meters cubed from the second term, then I'd be ok and all the units would be cancelled. But that crazy 2nd term with the 3/2 exponent gives me a crazy result for units, no matter what I do. I've tried expressing electron mass in both kilograms and electronvolts, and I've tried expressing Planck's constant in both electronvolts and in Joules, and no matter what I do, I end up with units like this: K3/2s6kg-3/2m-6
Stuff like that. That's no where near being able to cancel, no matter what I do.
So even ignoring the fact that the units don't cancel, I still don't get the result that's in the solution manual.
If anyone here has had experience with the Saha equation, you've probably done something like this and dealt with this problem before. It seems unavoidable.
Thanks.
 

Attachments

  • saha.jpg
    saha.jpg
    4.9 KB · Views: 513
  • prob.jpg
    prob.jpg
    42.9 KB · Views: 482
Physics news on Phys.org
  • #2
It's been a while since I had Stellar Astrophysics, but let's see:

mass of the electron should be in eV/c2 (I like eV better than SI units)
k is eV/K
T is K
h is eV⋅s

so that's eV/c2⋅eV/K⋅K/(eV⋅s)2 all to the 3/2

looks like everything cancels except c2 and s2, but c2=m2/s2 so all you're left with is (m2)3/2, which is just meters cubed. But, Pe is a density right? So, that is something per meters cubed which will cancel... I think. But, I don't think I made any mistakes in there.
 
  • Like
Likes leroyjenkens
  • #3
Sorry it's (1/(m2))3/2
 
  • Like
Likes leroyjenkens
  • #4
Chris B said:
Sorry it's (1/(m2))3/2
Thanks a lot. Turns out I wrote down the equation wrong, so every time I referenced the equation to see if I had it right, I kept looking at the wrong one that didn't include k in the numerator.
Thanks.
 
  • Like
Likes Chris B

1. What is the Saha Equation?

The Saha Equation is a mathematical formula used in astrophysics to describe the ionization of elements in a gaseous environment. It relates the ionization fraction of an element to the temperature, density, and ionization energy of that element.

2. Why do we need to use constants in the Saha Equation?

The Saha Equation includes several constants, such as the Boltzmann constant and the electron mass, which are necessary for accurately calculating the ionization fraction. These constants represent fundamental physical properties that remain constant in different environments and are essential for understanding the behavior of ionized gases.

3. What are the most important constants to use in the Saha Equation?

The most important constants in the Saha Equation are the gas constant, Boltzmann constant, electron mass, and Planck constant. These constants are vital in determining the ionization fraction of an element and are commonly used in astrophysics and other fields of science.

4. How do we determine the values of these constants?

The values of the constants used in the Saha Equation are well-established and can be found in reference tables or online databases. These values have been experimentally measured and are considered fundamental physical constants, meaning they do not change in different environments.

5. Can we use different values for the constants in the Saha Equation?

No, the values of the constants used in the Saha Equation are fixed and cannot be changed. Using different values would result in inaccurate calculations and predictions. However, there may be slight variations in the values used depending on the unit system or the precision required for a specific calculation.

Similar threads

B Exploring the equivalences between mass, time and length
    • Other Physics Topics
Replies
8
Views
498
MTW Box 21.1 - What can "add and subtract" do for Equation (12)?
    • Advanced Physics Homework Help
Replies
6
Views
890
A Trig functions and the gyroscope
    • Classical Physics
Replies
7
Views
843
Calculations using the Standard Solar Model & Solar Equations of State
    • Advanced Physics Homework Help
Replies
1
Views
859
I Is "nondimensionalization" a misnomer?
    • Other Physics Topics
Replies
19
Views
1K
Using Noether's theorem to get a constant of motion
    • Advanced Physics Homework Help
3
Replies
81
Views
6K
Deriving the kinetic energy flux in an effusion process
    • Advanced Physics Homework Help
Replies
4
Views
1K
Equation for neutrons in a nuclear reactor
    • Advanced Physics Homework Help
Replies
0
Views
35
Saha ionization equation I plug in the #, i still dont get same answer
    • Advanced Physics Homework Help
Replies
1
Views
2K
Why is solid density used in this thermodynamics problem?
    • Advanced Physics Homework Help
Replies
5
Views
946

Hot Threads

Recent Insights

Back
Top