1 D = 10^-18 statC·cm
= 10^-10 esu·Å
= 1⁄299,792,458×10^−21 C·m
≈ 3.33564×10^−30 C·m
≈ 1.10048498×1023
≈ 0.393430307 au
A dipole of 1 Debye is equal to 3.33 x 10-30 C m . Show that in atomic units 1 D = 0.39345 au.
The above is the deriviation that I found online, and the question says show this in atomic units, I don't really understand what its saying. Can you help please thanks.
Certainly! I can help you understand how to show that 1 Debye (D) is equal to 0.39345 atomic units (au).
To understand what "atomic units" means in this context, we need to have some background knowledge. Atomic units are a system of natural units that simplify calculations in quantum mechanics. In atomic units, certain fundamental physical constants, such as the electron mass, charge, and the speed of light, are normalized to 1.
Now, let's go through the derivation you mentioned step by step:
1. Start with the given value: 1 D = 3.33564×10^−30 C m.
2. Use the conversion factor provided in the derivation: 1 C m ≈ 1.10048498×10^23 atomic units (au).
To convert from C m to au, divide 1 D by this conversion factor:
1 D / (1.10048498×10^23 au) ≈ 3.33564×10^−30 C m / (1.10048498×10^23 au)
This gives you the value in atomic units.
3. Calculate this division to find the value in atomic units:
≈ 3.33564×10^−30 / 1.10048498×10^23 C m / au
≈ 3.028×10^-53 C m / au
≈ 3.028×10^-53 au
Therefore, you find that 1 Debye is approximately equal to 3.028×10^-53 atomic units.
To show that 1 D ≈ 0.39345 au, you need to compare this value with the given approximation. It seems that there may be a small rounding error in the given derivation. The correct approximation is actually:
1 Debye ≈ 3.028×10^-53 au
So, the statement that 1 Debye is equal to 0.39345 au is not accurate based on the given derivation. The correct value should be approximately 3.028×10^-53 au.