The radioactive element technetium is not found naturally on Earth; it must be synthesized in the laboratory. It is a valuable element, however, because it has medical uses. For example, the element in the form of sodium pertechnetate (NaTcO₄) is used in imaging studies of the brain, thyroid, and salivary glands and in renal blood flow studies, among other things. 

(a) In what group and period of the periodic table is the element found? 

(b) The valence electrons of technetium are found in the 5s and 4d subshells. What is a set of quantum numbers (n, ℓ, and m_ℓ) for one of the electrons of the 5s subshell? 

(c) Technetium emits a γ-ray with an energy of 0.141 MeV. (1 MeV = 10⁶ electron-volts, where 1 eV = 1.6022 × 10⁻¹⁹ J.) What are the wavelength and frequency of a γ-ray photon with an energy of 0.141 MeV?

(d) To make NaTcO₄, the metal is dissolved in nitric acid. 

and the product, HTcO₄, is treated with NaOH to make NaTcO₄. 

(i) Write a balanced equation for the reaction of HTcO₄ with NaOH. 

(ii) If you begin with 4.5 mg of Tc metal, what mass of NaTcO₄ can be made? What mass of NaOH, in grams, is required to convert all of the HTcO₄ into NaTcO₄? 

(e) If you synthesize 1.5 micromoles of NaTcO₄, what mass of compound do you have? If the compound is dissolved in 10.0 mL of solution, what is the concentration?

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7 HNO3(aq) + Tc(s) →→ HTCO4(aq) + 7 NO₂(g) + 3 H₂O(l)