Question

the maximum number of electrons that the 2nd energy level an atom can hold is
8
10
2
32
question 2
1 pts
an electron in a 3d orbital could have which of the following quantum numbers?
n = 3, l = 3, m_l = 1
n = 2, l = 2, m_l = 2
n = 3, l = 2, m_l = -3
n = 3, l = 2, m_l = 0

Explanation:

First Question

Step1: Recall the formula for electron capacity

The formula for the maximum number of electrons in an energy level \(n\) is \(2n^{2}\).

Step2: Substitute \(n = 2\) into the formula

When \(n=2\), we calculate \(2\times(2)^{2}\).
First, \(2^{2}=4\), then \(2\times4 = 8\).

Step1: Analyze the principal quantum number \(n\)

For a \(3d\) orbital, the principal quantum number \(n = 3\). So we can rule out the option with \(n = 2\) (the second option \(n = 2,l = 2,m_{l}=2\)).

Step2: Analyze the angular - momentum quantum number \(l\)

For \(d\) orbitals, \(l = 2\). So we can rule out the option with \(l=3\) (the first option \(n = 3,l = 3,m_{l}=1\)).

Step3: Analyze the magnetic quantum number \(m_{l}\)

The range of \(m_{l}\) is \(-l\leq m_{l}\leq l\). Since \(l = 2\), \(m_{l}\) can be \(- 2,-1,0,1,2\). So we can rule out the option with \(m_{l}=-3\) (the third option \(n = 3,l = 2,m_{l}=-3\)).

Answer:

8

Second Question