Question

learning goal:
to understand the energy levels in atoms.
in an atom, each electron has a fixed energy known as its energy level. for example, n = 1, n = 2, and n = 3 are energy levels. within each energy level, there are sublevels such as s, p, d, and f. within each sublevel, there are a certain number of orbitals.

part a
what is the maximum number of electrons that can be contained in the first, second, third, and fourth energy levels, respectively?
express your answer as integers separated by commas.
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submit

part b
enter the maximum number of electrons in each type of sublevel (s, p, d, and f, respectively)
express your answer as integers separated by commas.
view available hint(s)

Explanation:

Part A

Step1: Recall the formula for electron capacity in energy level \( n \)

The maximum number of electrons in an energy level \( n \) is given by the formula \( 2n^2 \).

Step2: Calculate for \( n = 1 \)

For \( n = 1 \), substitute into the formula: \( 2(1)^2 = 2(1)=2 \).

Step3: Calculate for \( n = 2 \)

For \( n = 2 \), substitute into the formula: \( 2(2)^2 = 2(4)=8 \).

Step4: Calculate for \( n = 3 \)

For \( n = 3 \), substitute into the formula: \( 2(3)^2 = 2(9)=18 \).

Step5: Calculate for \( n = 4 \)

For \( n = 4 \), substitute into the formula: \( 2(4)^2 = 2(16)=32 \).

Step1: Recall electron capacity of each sublevel

• The \( s \) sublevel has 1 orbital, and each orbital can hold a maximum of 2 electrons, so \( s \) can hold \( 1\times2 = 2 \) electrons.
• The \( p \) sublevel has 3 orbitals, so the number of electrons is \( 3\times2=6 \).
• The \( d \) sublevel has 5 orbitals, so the number of electrons is \( 5\times2 = 10 \).
• The \( f \) sublevel has 7 orbitals, so the number of electrons is \( 7\times2=14 \).

Answer:

2, 8, 18, 32

Part B