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.
To show that in atomic units (au), 1 Debye (D) is equal to 0.39345 au, we can follow these steps:
Step 1: Understand the conversion factor
Given that 1 Debye is equal to 3.33 x 10^-30 C m, we need to convert this to atomic units. Atomic units (au) is a system of natural units commonly used in atomic and molecular physics calculations.
Step 2: Convert the Debye value to atomic units
To convert a physical quantity from one unit to another, we need to know the conversion factor. In this case, we need to find the conversion factor between Debye and atomic units.
In atomic units, the electric charge unit (e) is defined as 1. The distance unit (a0) is the Bohr radius, which is approximately equal to 0.52918 Angstroms. The constant 4πε0 (where ε0 is the vacuum permittivity) is equal to 1 in atomic units.
Step 3: Use the conversion factor to calculate the value in atomic units
To convert the 1 Debye value to atomic units, we can multiply the given value by the appropriate conversion factor.
Conversion factor:
1 Debye = (3.33 x 10^-30 C m) / (1.602 x 10^-19 C/e) / (0.52918 x 10^-10 m/a0)
Step 4: Simplify the conversion factor
Simplifying the conversion factor, we get:
1 Debye = (3.33 x 10^-30 C m) / (1.602 x 10^-19 C/e) / (0.52918 x 10^-10 m/a0)
= (3.33 x 10^-30) / (1.602 x 10^-19) / (0.52918 x 10^-10) e a0
Step 5: Calculate the numerical value in atomic units
Calculating the numerical value, we get:
1 Debye = 0.39345 e a0
Step 6: Conclusion
Therefore, we have shown that 1 Debye is equal to 0.39345 atomic units (au).