Question

The Morse potential energy, alpha, has units of inverse length. Convert alpha = 2.10 [au of length]^-1. a) Units of [Angstroms]^-1 b) Units of [meters]^-1

Answer 1

Answer)

a)           1 au = 1 astronomical unit of length = 1.496 x 10¹¹ m                 ....(1)

              and 1 Angstroms = 10^-10 m                                                      ....(2)

              So 1 m = 10¹⁰ Angstroms                                                        ....(3)

             so 1 au = 1.496 x 10¹¹ m = 1.496 x 10¹¹ x 10¹⁰ Angstrom          ....(4)

                 So, 1 au = 1.496 x 10²¹ Angstroms                                       ....(5)

Now take inverse on both sides of (5), and we will get,

                           1 au^-1    = (1.496 x 10²¹)^-1 Angstrom^-1 = 0.668 x 10^-21 Angstrom^-1                ...(6)

So 2.10 au^-1 = 2.10 x 0.668 x 10^-21 Angstrom^-1 = 1.403 x 10^-21 Angstrom^-1

b) From (1)    1 au = 1 astronomical unit of length = 1.496 x 10¹¹ m      

Now take inverse on both sides of (1), and we will get,

                           1 au^-1    = (1.496 x 10¹¹)^-1 m^-1 = 0.668 x 10^-11 m^-1             .....(7)

Multiply both sides of (7) by 2.10

                             2.10 au^-1   =     2.10 x 0.668 x 10^-11 m^-1 = 1.403 x 10^-11 m^-1