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Chapter 2: Problem 43

Do both members of the following pairs have the same number of protons? Neutrons? Electrons? (a) \({ }_{1}^{2} \mathrm{H}\) and \({ }_{2}^{2} \mathrm{He}\) (b) \({ }_{6}^{14} \mathrm{C}\) and \({ }_{7}^{15} \mathrm{~N}\) (c) \({ }^{10} \mathrm{~F}\) and \({ }_{9}^{18} \mathrm{~F}\) Which pair(s) consist(s) of atoms with the same \(Z\) value? \(N\) value? \(A\) value?

Short Answer

Expert verified
(b) has the same N value (8). (c) has the same Z value (9). None have the same A value.

Step by step solution

01

Identify given values

Identify how many protons (Z), neutrons (N), and mass number (A) for each atom: (a) \(_{1}^{2} \mathrm{H}\) and \(_{2}^{2} \mathrm{He}\) (b) \(_{6}^{14} \mathrm{C}\) and \(_{7}^{15} \mathrm{~N}\) (c) \(_{9}^{10} \mathrm{F}\) and \(_{9}^{18} \mathrm{~F}\)
02

- Calculate Protons (Z)

Determine the number of protons, which is the atomic number (Z): (a1) \(_{1}^{2} \mathrm{H}\) has Z=1 (a2) \(_{2}^{2} \mathrm{He}\) has Z=2 (b1) \(_{6}^{14} \mathrm{C}\) has Z=6 (b2) \(_{7}^{15} \mathrm{~N}\) has Z=7 (c1) \(_{9}^{10} \mathrm{F}\) has Z=9 (c2) \(_{9}^{18} \mathrm{~F}\) has Z=9.
03

- Calculate Neutrons (N)

Calculate the number of neutrons using N = A - Z: (a1) \(_{1}^{2} \mathrm{H}\) has N = 2 - 1 = 1 (a2) \(_{2}^{2} \mathrm{He}\) has N = 2 - 2 = 0 (b1) \(_{6}^{14} \mathrm{C}\) has N = 14 - 6 = 8 (b2) \(_{7}^{15} \mathrm{~N}\) has N = 15 - 7 = 8 (c1) \(_{9}^{10} \mathrm{F}\) has N = 10 - 9 = 1 (c2) \(_{9}^{18} \mathrm{~F}\) has N = 18 - 9 = 9.
04

- Calculate Electrons

Determine the number of electrons in a neutral atom, which is equal to the number of protons (Z): (a1) \(_{1}^{2} \mathrm{H}\) has 1 electron (a2) \(_{2}^{2} \mathrm{He}\) has 2 electrons (b1) \(_{6}^{14} \mathrm{C}\) has 6 electrons (b2) \(_{7}^{15} \mathrm{~N}\) has 7 electrons (c1) \(_{9}^{10} \mathrm{F}\) has 9 electrons (c2) \(_{9}^{18} \mathrm{~F}\) has 9 electrons.
05

Compare Members of Each Pair

Compare each pair: (a) They do not have the same proton, neutron, or electron count. (b) They have the same neutron count (8) but different proton and electron counts. (c) They have the same proton and electron counts (9) but different neutron counts.
06

Identify Pairs with Same Values

Check which pairs have the same Z (proton), N (neutron), or A (mass number) values: (b) These have the same N value. (c) These have the same Z value. None of the pairs have the same A value.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Protons
Atoms are defined by the number of protons they contain, which is known as the atomic number (Z). Protons are positively charged particles located in the nucleus of an atom. The number of protons determines the element鈥檚 identity on the periodic table.
For example:
  • In the isotope \( \_{1}^{2}H \) (hydrogen), there is 1 proton.

  • In \( \_{2}^{2}He \) (helium), there are 2 protons.
  • Protons are crucial because they define what element the atom belongs to.
    In pairs (a) and (b), the first atoms (\( \_{1}^{2}H \) and \( \_{6}^{14}C \)) have different numbers of protons compared to their pair, showing they are different elements.
    Pair (c) shows \( \_{9}^{10}F \) and \( \_{9}^{18}F \) each have 9 protons, indicating these are isotopes of fluorine.
Neutrons
Neutrons are neutral particles located in the atom's nucleus alongside protons. The number of neutrons can vary within atoms of the same element, leading to different isotopes.
Neutrons stabilize the nucleus, and their count is calculated by subtracting the proton number from the mass number (A):
\( N = A - Z \).
  • For \( \_{1}^{2}H \), Neutrons (N) = 2 - 1 = 1.
    The number of neutrons alters the mass of the atom without changing its chemical properties.
    In our problem:
    Pair (b) \( \_{6}^{14}C \) and \( \_{7}^{15}N \) have the same number of neutrons, which is 8.
Electrons
Electrons are negatively charged particles that orbit the nucleus. In a neutral atom, the number of electrons is equal to the number of protons. Electrons determine the chemical behavior of an atom because they are involved in chemical bonds and reactions.In each pair, the electron count can be deduced:
  • For Pair (a), \( \_{1}^{2}H \) (1 electron) and \( \_{2}^{2}He \) (2 electrons) do not have the same numbers of electrons.
    The difference in their electron count signifies different chemical properties.
    In pair (c), \( \_{9}^{10}F \) and \( \_{9}^{18}F \) both have 9 electrons each.Thus, this pair has the same electron count but different neutron numbers, identifying them as isotopes.
Atomic Number (Z)
The atomic number or proton number (Z) uniquely identifies a chemical element. It indicates the number of protons in an atom's nucleus and, correspondingly, the number of electrons in a neutral atom.Examples in our problem:
  • For Pair (a), \( \_{1}^{2}H \) and \( \_{2}^{2}He \), Z = 1 and 2 gets different elements.
    I pair (c), \( \_{9}^{10}F \) and \( \_{9}^{18}F \), Z = 9. Since they have the same proton count, these are isotopes of fluorine.
Mass Number (A)
The mass number (A) is the total count of protons and neutrons in the nucleus of an atom:
\( A = Z + N \).
Distinct isotopes of an element can be identified by their different mass numbers, which reflect the difference in neutron count.
  • In Pair (b), \( \_{6}^{14}C \) and \( \_{7}^{15}N \) have distinct mass numbers of 14 and 15, respectively.
    This difference highlights that \( \_{6}^{14}C \) has 6 protons and 8 neutrons, while \( \_{7}^{15}N \) has 7 protons and 8 neutrons.
    None of our given pairs (a, b, or c) share the same mass number, indicating their distinct identity as different isotopes or elements.

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