Question

ments east atoms ame ferent rons mple, hich is that of all of ighted
₆¹²c ₆¹³c ₆¹⁴c
no. of neutrons
mass number
abundance 98.93 % 1.07 % <0.001 %
.9893x12=11.8716 .0107x13=.1391 .0001 x 12=.012
average atomic mass = 12.01 g/mol

Explanation:

To determine the number of neutrons and mass number for each carbon isotope, we use the following concepts:

For \( \boldsymbol{_6^{12}C} \):

Step1: Calculate number of neutrons

The formula for number of neutrons is \( \text{Number of neutrons} = \text{Mass number} - \text{Atomic number} \).
Atomic number of carbon (\( Z \)) is 6, mass number (\( A \)) is 12.
\( \text{Neutrons} = 12 - 6 = 6 \).

Step2: Identify mass number

Mass number is given as 12 (from \( _6^{12}C \)).

For \( \boldsymbol{_6^{13}C} \):

Step1: Calculate number of neutrons

Using \( \text{Neutrons} = A - Z \), with \( A = 13 \), \( Z = 6 \).
\( \text{Neutrons} = 13 - 6 = 7 \).

Step2: Identify mass number

Mass number is 13 (from \( _6^{13}C \)).

For \( \boldsymbol{_6^{14}C} \):

Step1: Calculate number of neutrons

Using \( \text{Neutrons} = A - Z \), with \( A = 14 \), \( Z = 6 \).
\( \text{Neutrons} = 14 - 6 = 8 \).

Step2: Identify mass number

Mass number is 14 (from \( _6^{14}C \)).

Filling the table:

Isotope	No. of neutrons	Mass Number
\( _6^{13}C \)	7	13
\( _6^{14}C \)	8	14

(Note: The last row in the given table appears to calculate the contribution of each isotope to the average atomic mass, using \( \text{Contribution} = \text{Abundance (decimal)} \times \text{Mass number} \). For example, for \( _6^{12}C \), \( 0.9893 \times 12 = 11.8716 \), and the total average atomic mass is the sum of these contributions: \( 11.8716 + 0.1391 + 0.012 \approx 12.01 \, \text{g/mol} \), which matches the given value.)

Answer:

To determine the number of neutrons and mass number for each carbon isotope, we use the following concepts:

For \( \boldsymbol{_6^{12}C} \):

Step1: Calculate number of neutrons

The formula for number of neutrons is \( \text{Number of neutrons} = \text{Mass number} - \text{Atomic number} \).
Atomic number of carbon (\( Z \)) is 6, mass number (\( A \)) is 12.
\( \text{Neutrons} = 12 - 6 = 6 \).

Step2: Identify mass number

Mass number is given as 12 (from \( _6^{12}C \)).

For \( \boldsymbol{_6^{13}C} \):

Step1: Calculate number of neutrons

Using \( \text{Neutrons} = A - Z \), with \( A = 13 \), \( Z = 6 \).
\( \text{Neutrons} = 13 - 6 = 7 \).

Step2: Identify mass number

Mass number is 13 (from \( _6^{13}C \)).

For \( \boldsymbol{_6^{14}C} \):

Step1: Calculate number of neutrons

Using \( \text{Neutrons} = A - Z \), with \( A = 14 \), \( Z = 6 \).
\( \text{Neutrons} = 14 - 6 = 8 \).

Step2: Identify mass number

Mass number is 14 (from \( _6^{14}C \)).

Filling the table:

Isotope	No. of neutrons	Mass Number
\( _6^{13}C \)	7	13
\( _6^{14}C \)	8	14

(Note: The last row in the given table appears to calculate the contribution of each isotope to the average atomic mass, using \( \text{Contribution} = \text{Abundance (decimal)} \times \text{Mass number} \). For example, for \( _6^{12}C \), \( 0.9893 \times 12 = 11.8716 \), and the total average atomic mass is the sum of these contributions: \( 11.8716 + 0.1391 + 0.012 \approx 12.01 \, \text{g/mol} \), which matches the given value.)