Ground state magnetic moment of 7Li

In summary, to calculate the ground state magnetic moment of 7Li, one can use the equation mu_J = gamma_J * J* hbar, with the spin value given as 3/2. The g_J factor can be calculated using the equation g_J = [g_l + (g_s - g_l)/(2l + 1)], where g_l and g_s are orbital and intrinsic spin g factors for the odd nucleon, and the upper sign is taken for J=/-1/2. Substituting the values of s, J, g_l and g_s, we can calculate the final value of mu_J to be 2.25185421746056 u_N.
  • #1
Stellar1
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Homework Statement


Calculate the ground state magnetic moment of 7Li using the below equations. The spin value is 3/2.


Homework Equations



mu_J = gamma_J * J* hbar = g_J * u_N

with g_J = [g_l + (g_s - g_l)/(2l + 1)]

where g_l and g_s are orbital and intrinsic spin g factors for the odd nucleon, l is orbital angular momentum and the upper sign is taken for J=/-1/2

The Attempt at a Solution



s = 3/2
J = l + s = l + 3/2
 
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  • #2
g_l = 0 g_s = 2.00231930436182mu_J = gamma_J * J* hbar = [g_l + (g_s - g_l)/(2l + 1)] * 3/2 * hbar= [0 + (2.00231930436182 - 0)/(2*2 + 1)] * 3/2 * hbar= 1.50123947827137 * 3/2 * hbar= 2.25185421746056 u_N
 

Related to Ground state magnetic moment of 7Li

1. What is the ground state magnetic moment of 7Li?

The ground state magnetic moment of 7Li refers to the magnetic moment of the lithium-7 atom when it is in its lowest possible energy state. It is a measure of the strength and direction of the magnetic field generated by the atom.

2. How is the ground state magnetic moment of 7Li calculated?

The ground state magnetic moment of 7Li is calculated by taking into account the spin of the nucleus and the spin of the electrons in the atom, as well as the orbital angular momentum of the electrons. These factors are combined using quantum mechanical equations to determine the overall magnetic moment.

3. What is the significance of the ground state magnetic moment of 7Li?

The ground state magnetic moment of 7Li is significant because it provides important information about the fundamental properties of the lithium-7 atom. It is also used in various theoretical and experimental studies, such as in nuclear magnetic resonance spectroscopy, to understand the behavior of atoms and molecules.

4. How does the ground state magnetic moment of 7Li compare to other elements?

The ground state magnetic moment of 7Li is relatively small compared to other elements. This is because lithium-7 has only three protons, which contribute to the overall magnetic moment, while other elements have more protons and therefore have a larger magnetic moment.

5. Can the ground state magnetic moment of 7Li be changed?

No, the ground state magnetic moment of 7Li is an intrinsic property of the lithium-7 atom and cannot be changed. However, the magnetic moment can be affected by external magnetic fields, which can cause the atom to transition to a higher energy state and therefore have a different magnetic moment.

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