Question

practice: isotope calculations #2

1. complete the following table.

isotopic symbol (nuclear form)	isotope symbol (hyphen form)	atomic #	mass #	# of protons	# of neutrons	# of electrons
			32	16
					24	20
$^{24}$mg
			64		34
	lead-207
		53	127
$^{238}$u
			129	52
		9	19

1. explain the difference between mass number and average atomic mass.
2. which tells you the most common version of an element?
3. place a star next to each column that represents an isotope that is the most common for that element.

atomic structure unit © 2017 star rocket science

Answer:

Part 1: Completing the Table

To complete the table, we use the following relationships:

• Atomic Number (\(Z\)) = Number of Protons = Number of Electrons (in neutral atoms).
• Mass Number (\(A\)) = Number of Protons + Number of Neutrons.
• Isotopic Symbol (Nuclear Form): \(\ce{^A_ZX}\) (where \(X\) is the element symbol).
• Isotopic Symbol (Hyphen Form): \(X\text{-}A\).

Row 1:

• Atomic # = 11 (Na, Sodium), Mass # = 24, Protons = 11, Electrons = 11.
• Neutrons = \(24 - 11 = 13\).
• Nuclear Form: \(\ce{^{24}_{11}Na}\), Hyphen Form: Sodium-24.

Row 2:

• Protons = 16 (S, Sulfur), Mass # = 32, Atomic # = 16.
• Neutrons = \(32 - 16 = 16\), Electrons = 16.
• Nuclear Form: \(\ce{^{32}_{16}S}\), Hyphen Form: Sulfur-32.

Row 3:

• Neutrons = 24, Electrons = 20 (so Protons = 20, Atomic # = 20, Ca, Calcium).
• Mass # = \(20 + 24 = 44\).
• Nuclear Form: \(\ce{^{44}_{20}Ca}\), Hyphen Form: Calcium-44.

Row 4: \(\ce{^{24}Mg}\)

• Mg (Magnesium) has Atomic # = 12 (Protons = 12, Electrons = 12).
• Mass # = 24, Neutrons = \(24 - 12 = 12\).
• Hyphen Form: Magnesium-24.

Row 5:

• Mass # = 64, Neutrons = 34, so Protons = \(64 - 34 = 30\) (Zn, Zinc, Atomic # = 30, Electrons = 30).
• Nuclear Form: \(\ce{^{64}_{30}Zn}\), Hyphen Form: Zinc-64.

Row 6: Lead-207

• Lead (Pb) has Atomic # = 82 (Protons = 82, Electrons = 82).
• Mass # = 207, Neutrons = \(207 - 82 = 125\).
• Nuclear Form: \(\ce{^{207}_{82}Pb}\).

Row 7:

• Atomic # = 53 (I, Iodine), Mass # = 127, Protons = 53, Electrons = 53.
• Neutrons = \(127 - 53 = 74\).
• Nuclear Form: \(\ce{^{127}_{53}I}\), Hyphen Form: Iodine-127.

Row 8: \(\ce{^{238}U}\)

• U (Uranium) has Atomic # = 92 (Protons = 92, Electrons = 92).
• Mass # = 238, Neutrons = \(238 - 92 = 146\).
• Hyphen Form: Uranium-238.

Row 9:

• Mass # = 129, Protons = 52 (Te, Tellurium, Atomic # = 52, Electrons = 52).
• Neutrons = \(129 - 52 = 77\).
• Nuclear Form: \(\ce{^{129}_{52}Te}\), Hyphen Form: Tellurium-129.

Row 10:

• Atomic # = 9 (F, Fluorine), Mass # = 19, Protons = 9, Electrons = 9.
• Neutrons = \(19 - 9 = 10\).
• Nuclear Form: \(\ce{^{19}_{9}F}\), Hyphen Form: Fluorine-19.

Part 2: Mass Number vs. Average Atomic Mass

• Mass Number: Integer (protons + neutrons) for a single isotope (e.g., Carbon-12 has mass number 12).
• Average Atomic Mass: Weighted average of masses of all naturally occurring isotopes of an element, in amu (e.g., average atomic mass of carbon is ~12.011 amu).

Part 3: Most Common Isotope Indicator

The average atomic mass (from the periodic table) tells you the most common isotope (since it is weighted by abundance). For example, carbon’s average atomic mass (~12.01) is closest to Carbon-12, so Carbon-12 is the most common.

Part 4: Identifying Most Common Isotopes

A star (\(*\)) is placed next to isotopes where the mass number is closest to the element’s average atomic mass (from the periodic table):

• \(\ce{^{24}Mg}\) (Mg: avg ~24.305) → *
• \(\ce{^{127}_{53}I}\) (I: avg ~126.90) → *
• \(\ce{^{19}_{9}F}\) (F: avg ~18.998) → *
• \(\ce{^{32}_{16}S}\) (S: avg ~32.06) → *

Final Table (Key Cells Filled):

Isotopic Symbol (Nuclear)	Isotope Symbol (Hyphen)	Atomic #	Mass #	# Protons	# Neutrons	# Electrons
\(\ce{^{32}_{16}S}\)	Sulfur-32	16	32	16	16	16
\(\ce{^{44}_{20}Ca}\)	Calcium-44	20	44	20	24	20
\(\ce{^{24}Mg}\)	Magnesium-24	12	24	12	12	12	*
\(\ce{^{64}_{30}Zn}\)	Zinc-64	30	64	30	34	30
\(\ce{^{207}_{82}Pb}\)	Lead-207	82	207	82	125	82
\(\ce{^{127}_{53}I}\)	Iodine-127	53	127	53	74	53	*
\(\ce{^{238}U}\)	Uranium-238	92	238	92	146	92
\(\ce{^{129}_{52}Te}\)	Tellurium-129	52	129	52	77	52
\(\ce{^{19}_{9}F}\)	Fluorine-19	9	19	9	10	9	*

(Note: Stars are placed based on average atomic mass proximity.)