Atom Structure Models

To solve the problem, we need to find the energy of the first orbit of a Li²⁺ ion, given the energy of the second orbit of a hydrogen atom.

1. Understanding the Energy Relation:
The energy of an electron in the nth orbit of a hydrogen-like atom is given by:

where:
- is the atomic number
- is the orbit number

2. Given Information:
Energy of second orbit of hydrogen atom = J
This corresponds to for :

3. Finding the Value of 1 eV in Joules:
From the above:

So,

4. Energy of First Orbit of Li²⁺:
For Li²⁺, ,

5. Convert Energy to Joules:

Final Answer:
The energy of the first orbit of Li²⁺ ion is .

To solve the problem, we need to find the number of electrons with values equal to 3, 4, and 5 for an element with atomic number .

1. Understanding the Quantum Numbers:
The quantum numbers (principal) and (azimuthal) define the energy levels and sublevels. The value helps determine the order of filling of orbitals. If two orbitals have the same value, the one with lower fills first.

2. Electron Configuration of Chromium (Z = 24):
The electronic configuration of Chromium (Z = 24) is:

This is due to the extra stability of half-filled .

3. Calculating Values:
We calculate for each orbital and count how many electrons have those values:

• : , → → 2 electrons
• : , → → 2 electrons
• : , → → 6 electrons
• : , → → 2 electrons
• : , → → 6 electrons
• : , → → 1 electron
• : , → → 5 electrons

4. Grouping by Values:
- → From and → Total = 6 + 2 = 8 electrons
- → From and → Total = 6 + 1 = 7 electrons
- → From → Total = 5 electrons

Final Answer:
The number of electrons with values of 3, 4, and 5 are , , and respectively.