Identify the element represented by each of the following symbols and give the number of protons and neutrons in each: \((\mathbf{a})_{33}^{74} X,(\mathbf{b}) \frac{1}{33} X$$(\mathbf{c})_{63}^{152} \mathrm{X},(\mathbf{d}) \frac{209}{83} \mathrm{X}\).

For each of the given symbols, we can use the atomic number (the subscript) to identify the element by referring to the periodic table. Since the number of protons in an atom determines its identity, the atomic number represents the number of protons in the element.

We already know that the atomic number represents the number of protons. To find the number of neutrons, we can subtract the atomic number from the atomic mass (the superscript). The atomic mass is the sum of the protons and neutrons in an atom.

(a) \(_{33}^{74} X\) Element: The atomic number is 33, which corresponds to the element Arsenic (As). Number of Protons: Atomic number = Number of protons = 33 Number of Neutrons: Atomic mass - Atomic number = Number of neutrons 74 - 33 = 41 Answer: Arsenic (As) with 33 protons and 41 neutrons. (b) \(^1_{33} X\) Element: The atomic number is 33, which corresponds to the element Arsenic (As). Number of Protons: Atomic number = Number of protons = 33 Number of Neutrons: Atomic mass - Atomic number = Number of neutrons 1 - 33 = -32 Answer: This symbol is not possible since the number of neutrons cannot be negative. (c) \(_{63}^{152} \mathrm{X}\) Element: The atomic number is 63, which corresponds to the element Europium (Eu). Number of Protons: Atomic number = Number of protons = 63 Number of Neutrons: Atomic mass - Atomic number = Number of neutrons 152 - 63 = 89 Answer: Europium (Eu) with 63 protons and 89 neutrons. (d) \(^{209}_{83} \mathrm{X}\) Element: The atomic number is 83, which corresponds to the element Bismuth (Bi). Number of Protons: Atomic number = Number of protons = 83 Number of Neutrons: Atomic mass - Atomic number = Number of neutrons 209 - 83 = 126 Answer: Bismuth (Bi) with 83 protons and 126 neutrons.