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Reduction: $Mn^{2+} + 2e^{-} \rightarrow Mn$ ($E^{0}_{red} = -1.18\text{ V}$)
Oxidation: $2Mn^{2+} \rightarrow 2Mn^{3+} + 2e^{-}$ ($E^{0}_{ox} = -1.51\text{ V}$)
$E^{0}_{cell} = E^{0}_{cathode} - E^{0}_{anode} = -1.18 - 1.51 = -2.69\text{ V}$. Since $E^{0}_{cell}$ is negative, the reaction is non-spontaneous.
Pender's Health Promotion Model (HPM, 1982; revised 1996) is grounded in social cognitive theory and emphasizes positive health behaviors rather than disease avoidance.
Key components of the HPM:
- Individual Characteristics and Experiences: Prior behavior, personal factors (biological, psychological, sociocultural)
- Behavior-Specific Cognitions and Affect: Perceived benefits, perceived barriers, perceived self-efficacy, activity-related affect, interpersonal and situational influences
- Behavioral Outcome: Commitment to a plan of action โ Health-promoting behavior
The senator's reputation, though initially _______ by false allegations of misconduct, ultimately emerged from the ordeal _______.
The sentence sets up a contrast: the reputation was harmed during the ordeal, but came out fine after it. Shaken...unscathed perfectly fits — 'shaken' means temporarily disturbed, and 'unscathed' means without lasting damage. 'Destroyed...intact' is contradictory. 'Damaged...impaired' gives no contrast. 'Tarnished...sullied' are both negative with no recovery implied.
For $h \ll R$, orbital radius $\approx R$.
Orbital velocity: $v_o = \sqrt{\frac{GM}{R}} = \sqrt{gR}$
Escape velocity from orbit at $R$: $v_e = \sqrt{\frac{2GM}{R}} = \sqrt{2gR}$
Minimum increase in speed:
$\Delta v = v_e - v_o = \sqrt{2gR} - \sqrt{gR} = \sqrt{gR}(\sqrt{2}-1)$
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