Determine the fractional abundance of each isotope.
This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
ScanSolve AI Answer
Here are the solutions to question 14:
14. (a) Calculate the relative atomic mass of element X.
Step 1: Determine the fractional abundance of each isotope.
The ratio of isotopes with masses 20 and 22 is 3:1.
Total parts in the ratio $= 3 + 1 = 4$.
Fractional abundance of isotope with mass 20 $= \frac{3}{4}$.
Fractional abundance of isotope with mass 22 $= \frac{1}{4}$.
Step 2: Calculate the relative atomic mass (RAM).
$$ \text{RAM} = (\text{mass of isotope 1} \times \text{fractional abundance 1}) + (\text{mass of isotope 2} \times \text{fractional abundance 2}) $$
$$ \text{RAM} = \left(20 \times \frac{3}{4}\right) + \left(22 \times \frac{1}{4}\right) $$
$$ \text{RAM} = \left(\frac{60}{4}\right) + \left(\frac{22}{4}\right) $$
$$ \text{RAM} = 15 + 5.5 $$
$$ \text{RAM} = 20.5 $$
The relative atomic mass of element X is $\boxed{\text{20.5}}$.
14. (b) Draw a labelled diagram showing the first three energy levels in an atom.
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NUCLEUS
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/|\
/ | \
/ | \
/ | \
/ | \
/ | \
/ | \
------------------- (n=1 or K shell)
----------------- (n=2 or L shell)
--------------- (n=3 or M shell)
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Diagram shows a central nucleus with three concentric circles representing the first three energy levels (shells), labelled n=1, n=2, n=3 or K, L, M.
14. (c) Explain the relationship between energy levels and orbitals.
Energy levels (also known as principal quantum shells) are the main regions around the nucleus where electrons are found, with higher numbers indicating higher energy and greater distance from the nucleus. Within each energy level, there are sub-levels (subshells), and each sub-level contains one or more orbitals. Orbitals are specific three-dimensional regions within a sub-level where there is a high probability of finding an electron. For example, the first energy level (n=1) contains only one s-orbital, while the second energy level (n=2) contains one s-orbital and three p-orbitals.
14. (d) State the order of filling of electrons into the first four orbitals.
The order of filling electrons into the first four orbitals according to the Aufbau principle is:
1s, 2s, 2p, 3s
