To determine how many electrons are present with \( m_l = 2 \) in the element Selenium (Se) with atomic number \( Z = 34 \), we will follow these steps:
### Step 1: Write the Electron Configuration
The first step is to write the electron configuration of Selenium. The atomic number \( Z = 34 \) indicates that Selenium has 34 electrons. The electron configuration is built by filling the orbitals in the order dictated by the Aufbau principle.
- The electron configuration for Selenium is:
\[
\text{Se: } [\text{Ar}] \, 3d^{10} \, 4s^2 \, 4p^4
\]
### Step 2: Identify the Relevant Orbitals
Next, we need to identify which orbitals correspond to the magnetic quantum number \( m_l = 2 \).
- The magnetic quantum number \( m_l \) can take values based on the orbital type:
- For \( s \) orbitals, \( m_l = 0 \)
- For \( p \) orbitals, \( m_l = -1, 0, +1 \)
- For \( d \) orbitals, \( m_l = -2, -1, 0, +1, +2 \)
From this, we see that \( m_l = 2 \) corresponds to the \( d \) orbital.
### Step 3: Count the Electrons in the \( d \) Orbital
Now, we look at the \( d \) orbital in the electron configuration.
- In the configuration \( 3d^{10} \), there are 10 electrons in the \( d \) orbital.
### Step 4: Determine the Electrons with \( m_l = 2 \)
Since the \( d \) orbital can hold a maximum of 10 electrons and \( m_l = 2 \) refers specifically to one of the five \( d \) orbitals (the \( d_{xy} \) orbital), we need to determine how many electrons occupy this specific orbital.
- In the \( 3d \) subshell, all five \( d \) orbitals are filled with 2 electrons each (due to Hund's rule and the Pauli exclusion principle), meaning:
- \( m_l = -2 \): 2 electrons
- \( m_l = -1 \): 2 electrons
- \( m_l = 0 \): 2 electrons
- \( m_l = +1 \): 2 electrons
- \( m_l = +2 \): 2 electrons
Thus, there are 2 electrons with \( m_l = 2 \).
### Final Answer
The number of electrons present with \( m_l = 2 \) in Selenium (Se) is:
\[
\text{Answer: } 2
\]
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