For the energy levels in an atom , which of the following statement is correct ?

Options

A. There are seven principle electron energy levels
B. The second principle energy levels has four sub-energy levels and contain a maximum of eight electron
C. The principle energy level 3 can have a maximum of `32` electrons
D. The 4s sub energy level has high energy than `3d` sub energy level

Answer

To determine which statement about the energy levels in an atom is correct, we will analyze each statement step by step.

### Step 1: Analyze the first statement
**Statement:** There are seven principal electron energy levels.

**Analysis:** This statement is correct. In atomic structure, the principal energy levels (or shells) are denoted by the principal quantum number \( n \). The values of \( n \) can be 1, 2, 3, 4, 5, 6, and 7, corresponding to the seven periods in the periodic table. Each principal energy level can contain different types of subshells (s, p, d, f, etc.).

### Step 2: Analyze the second statement
**Statement:** The second principal energy level has four sub-energy levels and contains a maximum of eight electrons.

**Analysis:** This statement is incorrect. The second principal energy level (\( n = 2 \)) has two sub-energy levels: the 2s and 2p subshells. The 2s subshell can hold a maximum of 2 electrons, and the 2p subshell can hold a maximum of 6 electrons, giving a total of 8 electrons. However, the claim that it has four sub-energy levels is incorrect.

### Step 3: Analyze the third statement
**Statement:** The principal energy level 3 can have a maximum of 32 electrons.

**Analysis:** This statement is also incorrect. The maximum number of electrons in a principal energy level is given by the formula \( 2n^2 \). For \( n = 3 \), the maximum number of electrons would be \( 2(3^2) = 18 \). The 3rd principal energy level has three subshells: 3s (2 electrons), 3p (6 electrons), and 3d (10 electrons), which sums to 18 electrons.

### Step 4: Analyze the fourth statement
**Statement:** The 4s sub-energy level has higher energy than the 3d sub-energy level.

**Analysis:** This statement is incorrect. To compare the energies of the 4s and 3d subshells, we can use the \( n + l \) rule. For 4s, \( n + l = 4 + 0 = 4 \), and for 3d, \( n + l = 3 + 2 = 5 \). Since a lower \( n + l \) value indicates lower energy, the 4s subshell has lower energy than the 3d subshell.

### Conclusion
After analyzing all four statements, we find that the first statement is correct: **There are seven principal electron energy levels.**

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