- #1

Flucky

- 95

- 1

1. Homework Statement

1. Homework Statement

## Homework Equations

Magnetic moment

*μ = g*

_{j}j μ_{N}Electric quadrupole moment

*Q ≈ -<r*

^{2}>[itex]\frac{2j - 1}{2(j + 1)}[/itex]## The Attempt at a Solution

So starting off with the isotopes of oxygen:

^{16}O,

^{17}O,

^{18}O

^{16}OThis fills the 1p[itex]\frac{1}{2}[/itex] shell.

spin = 0 because it is even-even

parity = 1 because even-even

μ = 0 because even-even

Q = 0 because it is a closed shell

^{18}OThis corresponds to the 1d[itex]\frac{5}{2}[/itex] shell.

Same values as above except for the electric quadrupole moment:

*Q ≈*

*-<r*-<r^{2}>[itex]\frac{2(0) - 1}{2((0) + 1)}[/itex] =^{2}>[itex]\frac{-1}{2}[/itex] = [itex]\frac{1}{2}[/itex]<r^{2}>

^{17}OThis corresponds to a valence neutron in the 1d[itex]\frac{5}{2}[/itex] shell.

spin = j = [itex]\frac{5}{2}[/itex]

parity = (-1)

^{l}= (-1)

^{2}= 1

μ = [itex]\frac{5}{2}[/itex]

*g*(I won't work out

_{j}μ_{N}*g*or put the value of

_{j}*μ*in)

_{N}*Q ≈*

*-<r*= -[itex]\frac{4}{7}[/itex]<r^{2}>[itex]\frac{2(\frac{5}{2}) - 1}{2((\frac{5}{2}) + 1)}[/itex]^{2}>