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Which two of the following isotopes have the same number of neutrons?

[tex]${ }_{16}^{34} S, { }_{16}^{32} S, { }_{17}^{35} Cl, { }_{18}^{38} Ar$[/tex]

A. [tex]${ }_{16}^{34} S$[/tex] and [tex]${ }_{16}^{32} S$[/tex]
B. [tex]${ }_{16}^{32} S$[/tex] and [tex]${ }_{17}^{35} Cl$[/tex]
C. [tex]${ }_{16}^{34} S$[/tex] and [tex]${ }_{17}^{35} Cl$[/tex]
D. [tex]${ }_{16}^{32} S$[/tex] and [tex]${ }_{18}^{38} Ar$[/tex]
E. [tex]${ }_{16}^{34} S$[/tex] and [tex]${ }_{18}^{38} Ar$[/tex]



Answer :

GinnyAnswer
To determine which two isotopes have the same number of neutrons, we need to calculate the number of neutrons in each of the given isotopes. The number of neutrons in an isotope can be found by subtracting the number of protons (atomic number) from the mass number.

Let's start with the isotopes given:

1. [tex]\({ }_{16}^{34} S\)[/tex]
- Number of protons [tex]\( (Z) \)[/tex]: 16
- Mass number [tex]\( (A) \)[/tex]: 34
- Number of neutrons [tex]\( (N) \)[/tex]: [tex]\( A - Z = 34 - 16 = 18 \)[/tex]

2. [tex]\({ }_{16}^{32} S\)[/tex]
- Number of protons [tex]\( (Z) \)[/tex]: 16
- Mass number [tex]\( (A) \)[/tex]: 32
- Number of neutrons [tex]\( (N) \)[/tex]: [tex]\( A - Z = 32 - 16 = 16 \)[/tex]

3. [tex]\({ }_{17}^{35} Cl\)[/tex]
- Number of protons [tex]\( (Z) \)[/tex]: 17
- Mass number [tex]\( (A) \)[/tex]: 35
- Number of neutrons [tex]\( (N) \)[/tex]: [tex]\( A - Z = 35 - 17 = 18 \)[/tex]

4. [tex]\({ }_{18}^{38} Ar\)[/tex]
- Number of protons [tex]\( (Z) \)[/tex]: 18
- Mass number [tex]\( (A) \)[/tex]: 38
- Number of neutrons [tex]\( (N) \)[/tex]: [tex]\( A - Z = 38 - 18 = 20 \)[/tex]

Now, we compare the number of neutrons for each of these isotopes:

- [tex]\({ }_{16}^{34} S\)[/tex] has 18 neutrons.
- [tex]\({ }_{16}^{32} S\)[/tex] has 16 neutrons.
- [tex]\({ }_{17}^{35} Cl\)[/tex] has 18 neutrons.
- [tex]\({ }_{18}^{38} Ar\)[/tex] has 20 neutrons.

From this comparison:

- Isotopes [tex]\({ }_{16}^{34} S\)[/tex] and [tex]\({ }_{17}^{35} Cl\)[/tex] both have 18 neutrons.

Therefore, the two isotopes that have the same number of neutrons are:
c. [tex]\({ }_{16}^{34} S\)[/tex] and [tex]\({ }_{17}^{35} Cl\)[/tex]

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