a helium atom is in one of its single states.one of the electrons is in an p-state and the other a D-sate.the atom is placed in a magnetic field,B,of strengh 3 tesla.
sketch a diagram showing the degenerated states and all permissible transition from D-state
b)Determine by how much the magnetic field changes the energy ofthe atom
To sketch a diagram showing the degenerate states and permissible transitions from the D-state of a helium atom in a magnetic field, follow these steps:
1. Start by drawing a box to represent the D-state.
2. Within the box, write the quantum numbers associated with the D-state. In this case, the principal quantum number (n) would be the same for both electrons, and for a D-state, n = 2.
3. Since the electrons are in different orbitals (p and D), write the azimuthal quantum number (l) for each electron. For the p-state, l = 1, and for the D-state, l = 2.
4. Include arrows within the box to represent the spin of each electron. They can be either up or down arrows, denoting the electron's spin-up or spin-down state.
5. Next, draw arrows outside the box to represent the possible transitions from the D-state. In a magnetic field, the orbital angular momentum of the electrons can change due to the interaction with the field, allowing for transitions between different magnetic sublevels.
- For an electron in the D-state (l = 2), there are five possible transitions:
i) D to D (no change in orbital angular momentum)
ii) D to P (change of ±1 in orbital angular momentum)
iii) D to F (change of ±2 in orbital angular momentum)
iv) D to G (change of ±3 in orbital angular momentum)
v) D to H (change of ±4 in orbital angular momentum)
Now, to determine how much the magnetic field changes the energy of the helium atom, we need to consider the Zeeman effect, which describes the splitting of energy levels in the presence of a magnetic field.
The change in energy (ΔE) can be calculated using the formula:
ΔE = gμBmB
Where:
- ΔE is the change in energy
- g is the Landé g-factor (also called the spectroscopic splitting factor)
- μB is the Bohr magneton (a constant)
- mB is the magnetic quantum number
In the case of the helium atom, the g-factor for the ground state is approximately 1.0, and the magnetic quantum number (mB) can have values from -2 to +2 for the D-state.
Using the given magnetic field strength of 3 Tesla, you can calculate the change in energy (ΔE) for each possible transition by plugging in the values of g, μB, and mB into the formula. Remember to consider both positive and negative values of mB for each transition.
Once you have the ΔE values for each transition, you can compare them to determine the energy change caused by the magnetic field.