Question

identify the parts of an atom
diagram of an atom with labeled arrows

subatomic particle	location in the atom	charge	weight
neutron	nucleus	(0)	1amu
electron	electron cloud	(-)	.0005amu (approx)

practice: calculate the average atomic mass for each isotope set. show your work.

element	isotope masses	percent abundance	average atomic mass
	2	0.015%
helium	3	0.0001%
	4	99.9999%
carbon	12	98.89%
	13	1.11%
oxygen	16	99.759%
	17	0.76%
	18	0.204%
sulfur	32	95.002%
	33	0.76%
	34	4.22%
	36	0.014%

Explanation:

To calculate the average atomic mass, we use the formula:
\[ \text{Average Atomic Mass} = \sum (\text{Isotope Mass} \times \text{Percent Abundance (in decimal)}) \]

Hydrogen

Step 1: Convert percentages to decimals

• Isotope 1: \( 99.985\% = 0.99985 \)
• Isotope 2: \( 0.015\% = 0.00015 \)

Step 2: Multiply and sum

\[ (1 \times 0.99985) + (2 \times 0.00015) = 0.99985 + 0.0003 = 1.00015 \, \text{amu} \]

Helium

Step 1: Convert percentages to decimals

• Isotope 3: \( 0.0001\% = 0.000001 \)
• Isotope 4: \( 99.9999\% = 0.999999 \)

Step 2: Multiply and sum

\[ (3 \times 0.000001) + (4 \times 0.999999) = 0.000003 + 3.999996 = 3.999999 \, \text{amu} \approx 4.0 \, \text{amu} \]

Carbon

Step 1: Convert percentages to decimals

• Isotope 12: \( 98.89\% = 0.9889 \)
• Isotope 13: \( 1.11\% = 0.0111 \)

Step 2: Multiply and sum

\[ (12 \times 0.9889) + (13 \times 0.0111) = 11.8668 + 0.1443 = 12.0111 \, \text{amu} \]

Oxygen

Step 1: Convert percentages to decimals

• Isotope 16: \( 99.759\% = 0.99759 \)
• Isotope 17: \( 0.76\% = 0.0076 \)
• Isotope 18: \( 0.204\% = 0.00204 \)

Step 2: Multiply and sum

\[ (16 \times 0.99759) + (17 \times 0.0076) + (18 \times 0.00204) \]
\[ = 15.96144 + 0.1292 + 0.03672 = 16.12736 \, \text{amu} \approx 16.00 \, \text{amu (approximate, slight rounding)} \]

Sulfur

Step 1: Convert percentages to decimals

• Isotope 32: \( 95.002\% = 0.95002 \)
• Isotope 33: \( 0.76\% = 0.0076 \)
• Isotope 34: \( 4.22\% = 0.0422 \)
• Isotope 36: \( 0.014\% = 0.00014 \)

Step 2: Multiply and sum

\[ (32 \times 0.95002) + (33 \times 0.0076) + (34 \times 0.0422) + (36 \times 0.00014) \]
\[ = 30.40064 + 0.2508 + 1.4348 + 0.00504 = 32.09128 \, \text{amu} \approx 32.07 \, \text{amu} \]

Final Answers:

• Hydrogen: \( \boldsymbol{1.00015 \, \text{amu}} \)
• Helium: \( \boldsymbol{\approx 4.0 \, \text{amu}} \)
• Carbon: \( \boldsymbol{12.0111 \, \text{amu}} \)
• Oxygen: \( \boldsymbol{\approx 16.00 \, \text{amu}} \) (or \( 16.13 \, \text{amu} \) without rounding)
• Sulfur: \( \boldsymbol{\approx 32.07 \, \text{amu}} \)

Answer:

To calculate the average atomic mass, we use the formula:
\[ \text{Average Atomic Mass} = \sum (\text{Isotope Mass} \times \text{Percent Abundance (in decimal)}) \]

Hydrogen

Step 1: Convert percentages to decimals

• Isotope 1: \( 99.985\% = 0.99985 \)
• Isotope 2: \( 0.015\% = 0.00015 \)

Step 2: Multiply and sum

\[ (1 \times 0.99985) + (2 \times 0.00015) = 0.99985 + 0.0003 = 1.00015 \, \text{amu} \]

Helium

Step 1: Convert percentages to decimals

• Isotope 3: \( 0.0001\% = 0.000001 \)
• Isotope 4: \( 99.9999\% = 0.999999 \)

Step 2: Multiply and sum

\[ (3 \times 0.000001) + (4 \times 0.999999) = 0.000003 + 3.999996 = 3.999999 \, \text{amu} \approx 4.0 \, \text{amu} \]

Carbon

Step 1: Convert percentages to decimals

• Isotope 12: \( 98.89\% = 0.9889 \)
• Isotope 13: \( 1.11\% = 0.0111 \)

Step 2: Multiply and sum

\[ (12 \times 0.9889) + (13 \times 0.0111) = 11.8668 + 0.1443 = 12.0111 \, \text{amu} \]

Oxygen

Step 1: Convert percentages to decimals

• Isotope 16: \( 99.759\% = 0.99759 \)
• Isotope 17: \( 0.76\% = 0.0076 \)
• Isotope 18: \( 0.204\% = 0.00204 \)

Step 2: Multiply and sum

\[ (16 \times 0.99759) + (17 \times 0.0076) + (18 \times 0.00204) \]
\[ = 15.96144 + 0.1292 + 0.03672 = 16.12736 \, \text{amu} \approx 16.00 \, \text{amu (approximate, slight rounding)} \]

Sulfur

Step 1: Convert percentages to decimals

• Isotope 32: \( 95.002\% = 0.95002 \)
• Isotope 33: \( 0.76\% = 0.0076 \)
• Isotope 34: \( 4.22\% = 0.0422 \)
• Isotope 36: \( 0.014\% = 0.00014 \)

Step 2: Multiply and sum

\[ (32 \times 0.95002) + (33 \times 0.0076) + (34 \times 0.0422) + (36 \times 0.00014) \]
\[ = 30.40064 + 0.2508 + 1.4348 + 0.00504 = 32.09128 \, \text{amu} \approx 32.07 \, \text{amu} \]

Final Answers:

• Hydrogen: \( \boldsymbol{1.00015 \, \text{amu}} \)
• Helium: \( \boldsymbol{\approx 4.0 \, \text{amu}} \)
• Carbon: \( \boldsymbol{12.0111 \, \text{amu}} \)
• Oxygen: \( \boldsymbol{\approx 16.00 \, \text{amu}} \) (or \( 16.13 \, \text{amu} \) without rounding)
• Sulfur: \( \boldsymbol{\approx 32.07 \, \text{amu}} \)