5.3 F and 5.3 G Solve for quotients of decimals to the hundredths

Evaluating function (3) - f(x)=9x+1 and g(x)=2x+5

Understanding Quantum Theory of Electrons in Atoms The goal of this section is to understand the electron orbitals (location of electrons in atoms), their different energies, and other properties. The use of quantum theory provides the best understanding to these topics. This knowledge is a precursor to chemical bonding. As was described previously, electrons in atoms can exist only on discrete energy levels but not between them. It is said that the energy of an electron in an atom is quantized, that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels. The energy levels are labeled with an n value, where n = 1, 2, 3, …. Generally speaking, the energy of an electron in an atom is greater for greater values of n. This number, n, is referred to as the principal quantum number. The principal quantum number defines the location of the energy level. It is essentially the same concept as the n in the Bohr atom description. Another name for the principal quantum number is the shell number. The shells of an atom can be thought of concentric circles radiating out from the nucleus. The electrons that belong to a specific shell are most likely to be found within the corresponding circular area. The further we proceed from the nucleus, the higher the shell number, and so the higher the energy level (Figure 9.4.1). The positively charged protons in the nucleus stabilize the electronic orbitals by electrostatic attraction between the positive charges of the protons and the negative charges of the electrons. So the further away the electron is from the nucleus, the greater the energy it has. This quantum mechanical model for where electrons reside in an atom can be used to look at electronic transitions, the events when an electron moves from one energy level to another. If the transition is to a higher energy level, energy is absorbed, and the energy change has a positive value. To obtain the amount of energy necessary for the transition to a higher energy level, a photon is absorbed by the atom. A transition to a lower energy level involves a release of energy, and the energy change is negative. This process is accompanied by emission of a photon by the atom. The following equation summarizes these relationships and is based on the hydrogen atom: The values nf and ni are the final and initial energy states of the electron. The principal quantum number is one of three quantum numbers used to characterize an orbital. An atomic orbital, which is distinct from an orbit, is a general region in an atom within which an electron is most probable to reside. The quantum mechanical model specifies the probability of finding an electron in the three-dimensional space around the nucleus and is based on solutions of the Schrödinger equation. In addition, the principal quantum number defines the energy of an electron in a hydrogen or hydrogen-like atom or an ion (an atom or an ion with only one electron) and the general region in which discrete energy levels of electrons in a multi-electron atoms and ions are located. Another quantum number is l, the angular momentum quantum number. It is an integer that defines the shape of the orbital, and takes on the values, l = 0, 1, 2, …, n – 1. This means that an orbital with n = 1 can have only one value of l, l = 0, whereas n = 2 permits l = 0 and l = 1, and so on. The principal quantum number defines the general size and energy of the orbital. The l value specifies the shape of the orbital. Orbitals with the same value of l form a subshell. In addition, the greater the angular momentum quantum number, the greater is the angular momentum of an electron at this orbital. Orbitals with l = 0 are called s orbitals (or the s subshells). The value l = 1 corresponds to the p orbitals. For a given n, p orbitals constitute a p subshell (e.g., 3p if n = 3). The orbitals with l = 2 are called the d orbitals, followed by the f-, g-, and h-orbitals for l = 3, 4, 5, and there are higher values we will not consider. There are certain distances from the nucleus at which the probability density of finding an electron located at a particular orbital is zero. In other words, the value of the wavefunction ψ is zero at this distance for this orbital. Such a value of radius r is called a radial node. The number of radial nodes in an orbital is n – l – 1. Consider the examples in Figure 9.4.2. The orbitals depicted are of the s type, thus l = 0 for all of them. It can be seen from the graphs of the probability densities that there are 1 – 0 – 1 = 0 places where the density is zero (nodes) for 1s (n = 1), 2 – 0 – 1 = 1 node for 2s, and 3 – 0 – 1 = 2 nodes for the 3s orbitals. The s subshell electron density distribution is spherical and the p subshell has a dumbbell shape. The d and f orbitals are more complex. These shapes represent the three-dimensional regions within which the electron is likely to be found. Principal quantum number (n) & Orbital angular momentum (l): The Orbital Subshell: https://youtu.be/ms7WR149fAY If an electron has an angular momentum (l ≠ 0), then this vector can point in different directions. In addition, the z component of the angular momentum can have more than one value. This means that if a magnetic field is applied in the z direction, orbitals with different values of the z component of the angular momentum will have different energies resulting from interacting with the field. The magnetic quantum number, called ml, specifies the z component of the angular momentum for a particular orbital. For example, for an s orbital, l = 0, and the only value of ml is zero. For p orbitals, l = 1, and ml can be equal to –1, 0, or +1. Generally speaking, ml can be equal to –l, –(l – 1), …, –1, 0, +1, …, (l – 1), l. The total number of possible orbitals with the same value of l (a subshell) is 2l + 1. Thus, there is one s-orbital for ml = 0, there are three p-orbitals for ml = 1, five d-orbitals for ml = 2, seven f-orbitals for ml = 3, and so forth. The principal quantum number defines the general value of the electronic energy. The angular momentum quantum number determines the shape of the orbital. And the magnetic quantum number specifies orientation of the orbital in space, as can be seen in Figure 9.4.3. Figure 9.4.4 illustrates the energy levels for various orbitals. The number before the orbital name (such as 2s, 3p, and so forth) stands for the principal quantum number, n. The letter in the orbital name defines the subshell with a specific angular momentum quantum number l = 0 for s orbitals, 1 for p orbitals, 2 for d orbitals. Finally, there are more than one possible orbitals for l ≥ 1, each corresponding to a specific value of ml. In the case of a hydrogen atom or a one-electron ion (such as He+, Li2+, and so on), energies of all the orbitals with the same n are the same. This is called a degeneracy, and the energy levels for the same principal quantum number, n, are called degenerate energy levels. However, in atoms with more than one electron, this degeneracy is eliminated by the electron–electron interactions, and orbitals that belong to different subshells have different energies. Orbitals within the same subshell (for example ns, np, nd, nf, such as 2p, 3s) are still degenerate and have the same energy. While the three quantum numbers discussed in the previous paragraphs work well for describing electron orbitals, some experiments showed that they were not sufficient to explain all observed results. It was demonstrated in the 1920s that when hydrogen-line spectra are examined at extremely high resolution, some lines are actually not single peaks but, rather, pairs of closely spaced lines. This is the so-called fine structure of the spectrum, and it implies that there are additional small differences in energies of electrons even when they are located in the same orbital. These observations led Samuel Goudsmit and George Uhlenbeck to propose that electrons have a fourth quantum number. They called this the spin quantum number, or ms. The other three quantum numbers, n, l, and ml, are properties of specific atomic orbitals that also define in what part of the space an electron is most likely to be located. Orbitals are a result of solving the Schrödinger equation for electrons in atoms. The electron spin is a different kind of property. It is a completely quantum phenomenon with no analogues in the classical realm. In addition, it cannot be derived from solving the Schrödinger equation and is not related to the normal spatial coordinates (such as the Cartesian x, y, and z). Electron spin describes an intrinsic electron “rotation” or “spinning.” Each electron acts as a tiny magnet or a tiny rotating object with an angular momentum, even though this rotation cannot be observed in terms of the spatial coordinates. The magnitude of the overall electron spin can only have one value, and an electron can only “spin” in one of two quantized states. One is termed the α state, with the z component of the spin being in the positive direction of the z axis. This corresponds to the spin quantum number ms=12. The other is called the β state, with the z component of the spin being negative and ms=−12. Any electron, regardless of the atomic orbital it is located in, can only have one of those two values of the spin quantum number. The energies of electrons having ms=−12 and ms=12 are different if an external magnetic field is applied. Figure 9.4.5 illustrates this phenomenon. An electron acts like a tiny magnet. Its moment is directed up (in the positive direction of the z axis) for the 12 spin quantum number and down (in the negative z direction) for the spin quantum number of −12. A magnet has a lower energy if its magnetic moment is aligned with the external magnetic field (the left electron) and a higher energy for the magnetic moment being opposite to the applied field. This is why an electron with ms=12 has a slightly lower energy in an external field in the positive z direction, and an electron with ms=−12 has a slightly higher energy in the same field. This is true even for an electron occupying the same orbital in an atom. A spectral line corresponding to a transition for electrons from the same orbital but with different spin quantum numbers has two possible values of energy; thus, the line in the spectrum will show a fine structure splitting. The Pauli Exclusion Principle An electron in an atom is completely described by four quantum numbers: n, l, ml, and ms. The first three quantum numbers define the orbital and the fourth quantum number describes the intrinsic electron property called spin. An Austrian physicist Wolfgang Pauli formulated a general principle that gives the last piece of information that we need to understand the general behavior of electrons in atoms. The Pauli exclusion principle can be formulated as follows: No two electrons in the same atom can have exactly the same set of all the four quantum numbers. What this means is that electrons can share the same orbital (the same set of the quantum numbers n, l, and ml), but only if their spin quantum numbers ms have different values. Since the spin quantum number can only have two values (±12), no more than two electrons can occupy the same orbital (and if two electrons are located in the same orbital, they must have opposite spins). Therefore, any atomic orbital can be populated by only zero, one, or two electrons. The properties and meaning of the quantum numbers of electrons in atoms are briefly

Chapter 22 Antihypertensive Drugs Hypertension Defined (JNC-8) Pharmacology Overview 7 main categories of drugs to treat HTN Adrenergic drugs (old friend) Angiotensin-converting enzyme (ACE) inhibitors Angiotensin II receptor blockers (ARBs) Calcium channel blockers (CCBs) Diuretics Vasodilators Direct renin inhibitors A. Adrenergic Drugs: 5 Subcategories and where they act A1. Adrenergic neuron blockers (central and peripheral)- we won’t talk about this A2. Alpha1 receptor blockers (peripheral) A3. Alpha2 receptor agonists (central) A4. Beta receptor blockers (peripheral) A5. Combined α and β receptor blockers (peripheral) A2. Peripherally Acting Adrenergic DrugAlpha1 Blockers (we’ve met these) Doxazosin, prazosin, alfuzosin Block alpha1-receptors which causes BP to decrease Reduces peripheral vascular resistance and BP by dilating both arterial and venous blood vessels Main Use: benign prostatic hyperplasia (BPH) Alpha1 Blockers REMEMBER Tamsulosin (Flomax)* is an α1 blocker BUT *Tamsulosin is not used to control BP, just for BPH. A3. Centrally Acting Adrenergic DrugsAlpha 2 agonist Clonidine and methyldopa 1- Stimulate alpha2-adrenergic receptors. in the brain Decreases sympathetic outflow from the CNS which decreases NE production 2. Stimulate alpha2-adrenergic receptors in kidneys remember alpha 2 opposes alpha 1 Dilates peripheral blood vessels → lowers peripheral resistance → Results in decreased BP So ….Clonidine (Catapres) Used primarily for its ability to decrease blood pressure in an urgent setting Also use in opioid withdrawal as previously discussed Oral (multiple times a day), and topical patch formulations Do not stop abruptly as it may lead to rebound hypertension In reality, Clonidine and methyldopa Not prescribed as first-line home antiHTN drugs High incidence of unwanted adverse effects: orthostatic hypotension, fatigue, and dizziness MIGHT be uses as adjunct drugs after other drugs have failed, in conjunction with other antiHTN such as diuretics A4. Adrenergic Drugs Selective Beta 1 Blockers Metoprolol, Atenolol Reduction of HR through β1 receptor blockade (remember adrenergic blocking of this receptor???) HR results in BP Cause reduced secretion of renin = BP A4. Adrenergic Drugs Selective Beta1 Blockers Nebivolol (Bystolic) Uses: hypertension and HF Action: blocks β1 receptors and produces vasodilatation, which results in a decrease in SVR High doses loses selectivity and blocks both β1 and β2 Less sexual dysfunction All BB- Do not stop abruptly; must be tapered over 1 to 2 weeks A4. Adrenergic Drugs NONSelective Beta Blockers Propranolol Acts equally on β1 and β2 Other uses include situational anxiety associated with public speaking, test taking As mentioned on previous slide, nebivolol at high doses becomes beta nonselective A5. Dual-Action Adrenergic Drugs α1 and β Receptor Blockers Dual antihypertensive effects of reduction in heart rate (beta1 receptor blockade) and vasodilation (alpha1 receptor blockade) Examples are carvedilol (common) and labetalol (not as common) A5. Dual-Action Adrenergic Drugs α1 and β Receptor Blockers Carvedilol (Coreg) Widely used drug that is well tolerated Uses: HTN, mild to moderate HF in conjunction with digoxin, diuretics, and ACE inhibitors Contraindications: severe bradycardia or unstable HF, bronchospastic conditions such as asthma, and various cardiac conduction problems Adrenergic Drugs Indications - HTN But also for Glaucoma (topical) BPH: doxazosin, prazosin, and terazosin (2 for 1) Management of severe HF when used with cardiac glycosides and diuretics Contraindications Acute HF- have to stabilize first MOAIs- yeah doesn’t everything interact with MAOIs? Peptic ulcers Severe liver/kidney disease Asthma (with beta blockers) Adrenergic Drugs: Adverse Effects Orthostatic hypotension 1st-dose syncope Rebound hypertension with abrupt discontinuation Most common: Dry mouth, drowsiness, constipation, sedation Interactions- always check for specific drug interactions Can cause additive CNS depression with alcohol, benzodiazepines, opioids Question #1 When administering an alpha-adrenergic drug for hypertension, it is most important for the nurse to assess the patient for the development of what response? Hypotension Hyperkalemia Oliguria Respiratory distress Answer A Hypotension This is a key point in patient education These drugs have strong vasodilating properties and may cause severe hypotension, especially at the beginning of therapy. B. Angiotensin-Converting Enzyme Inhibitorsaka ACE Inhibitors or ACEi Large group of safe and effective drugs Currently are 10 ACEi Often used as first-line drugs for HF and hypertension May be combined with a thiazide diuretic, loop diuretic, or Calcium Channel Blocker (CCB) You need to understand the basics ACE Inhibitors: Review RAAS ACE converts angiotensin I, formed through the action of renin, to angiotensin II Angiotensin 2 is a potent vasoconstrictor and also induces aldosterone secretion by the adrenal glands Aldosterone stimulates sodium resorption (H20 follows Na Both act to raise BP which causes kidneys to reduce renin production ACEi= Great drug to treat HTN BUT contraindicated in pregnancy (2nd,3rd trimester due to fetal renal damage) and breastfeeding first few weeks after birth B. ACE Inhibitors - PRIL Lisinopril (Prinivil) super common, often the 1st drug Enalapril (Vasotec) also common Captopril (Capoten) great if liver disease present Benazepril (Lotensin) Fosinopril (Monopril) Perindopril (Aceon) Quinapril (Accupril) Ramipril (Altace) Trandolapril (Mavik) Primary Effects of the ACE Inhibitors Prevent Na (and H2O) resorption by inhibiting aldosterone secretion (volume reduction) (GO BACK TO RAAS DIAGRAM) blood volume decreases work of the heart preload, or the left ventricular end-diastolic volume which is important in HF ACE SUMMARY OF ACTIVITY 1) Prevent vasoconstriction caused by angiotensin 2 (2) Prevent aldosterone secretion  less sodium and water resorption Cardioprotective Effects of ACEi They slow progression of left ventricular hypertrophy (ventricular remodeling) after MI so considered cardioprotective ACE inhibitors have been shown to decrease morbidity and mortality in patients with HF Renal Protective Effects of ACEi ACE inhibitors: reduce glomerular filtration pressure by volume reduction Cardiovascular drug of choice for patients with diabetes since it helps protect kidneys by reducing pressure. Sometimes used low dose for kidney protection with DM without HTN B. ACEi Enalapril (Vasotec) Only ACEi available in both oral and IV Enalapril IV does not require cardiac monitoring Oral enalapril: prodrug (metabolized in liver) Improves patient’s chances of survival after an MI Reduces the incidence of HF B. ACEi Captopril (Capoten) Uses: prevention of ventricular remodeling after MI; reduce the risk of HF after MI Shortest half-life Must be administered multiple times throughout the day so this limits its use Not a prodrug so good for patient with liver disease Question #2 A patient with diabetes has a new prescription for the ACE inhibitor lisinopril. She questions this order because her provider has never told her that she has hypertension. What is the best explanation for this order? The doctor knows best The patient is confused This medication has cardioprotective properties This medication has a protective effect on the kidneys for patients with diabetes Answer D ACE inhibitors have been shown to have a protective effect on the kidneys because they reduce glomerular filtration pressure. This property makes them the cardiovascular drug of choice for patients with diabetes. Question #3 A patient with a history of pancreatitis and cirrhosis is also being treated for hypertension. Which drug will most likely be ordered for this patient? Clonidine Prazosin Diltiazem Captopril Answer D Captopril Captopril is not a prodrug; therefore, it does not need to be metabolized by the liver to be effective. This is an advantage in patients with liver disease. ACE Inhibitors: Adverse Effects *Dry, nonproductive cough, which reverses when therapy is stopped. This is a class effect Dizziness- Note: First-dose hypotensive effect may occur Headache & Fatigue Possible hyperkalemia ** Angioedema: rare but potentially fatal Not safe in pregnancy-are contraindicated during the second and third trimesters of pregnancy because of increased risk of fetal renal damage C. Angiotensin II Receptor Blockers(ARB) Considered an alternative to ACEi Less likely to cause a dry cough and hyper K+ that is common with ACE inhibitors Angiotensin II Receptor Blockers: Mechanism of Action Go back to RAAS diagram! ARBs affect primarily 2 places 1. Vascular smooth muscle - blocks vasoconstriction 2. Adrenal gland -Selectively blocks the binding of Ang 2 to certain Ang 2 receptors inhibiting secretion of aldosterone Lowers volume retention and BP Angiotensin II Receptor Blockers -ARTAN Losartan (Cozaar)- very common Eprosartan (Teveten) Valsartan (Diovan) Irbesartan (Avapro) Candesartan (Atacand) Olmesartan (Benicar) Telmisartan (Micardis) Azilsartan (Edarbi) C. ARB Losartan (Cozaar) Beneficial in patients with HTN and HF Used with caution in patients with kidney or liver dysfunction and in patients with renal artery stenosis ***Not safe for breastfeeding women and should not be used in pregnancy (Cat C 1st trimester, Cat D 2nd-3rd trimester), potential fetal toxicity Appear to be equally effective for the treatment of hypertension and well tolerated ARBs less likely to cause cough and hyperK+ but can still happen Evidence that ARBs are associated with lower mortality after MI than ACE inhibitors Never take ACEi and ARBs at the same time* 5. Calcium Channel Blockers (CCB) Primary use: HTN, angina, some dysrhythmias Cause smooth muscle relaxation by blocking the binding of calcium to its receptors, preventing muscle contraction Results in: Relaxed blood vessels to the heart Decreased peripheral smooth muscle tone Decreased SVResistance Decreased BP E. Diuretics First-line antiHTN in JNC 8 guidelines Decreases fluid volume The results from diuresis: preload, Peripheral resistance Overall effect  Decreased workload of the heart and decreased BP Thiazide diuretics are the most commonly used diuretics for HTN Ie hydrochlorothiazide (HCTZ), chlorthalidone We will discuss diuretics further in the chapter on diuretics F. Vasodilators Directly relax arterial or venous smooth muscle (or both) Results in: Decreased SVR Decreased afterload Peripheral vasodilation Indicated for treatment of HTN May be used in combination with other drugs F. Vasodilators Hydralazine (Apresoline) Orally: routine cases of essential hypertension Injectable: hypertensive emergencies BiDil: specifically indicated as an adjunct for treatment of HF in African-American patients F. Vasodilators Sodium Nitroprusside (Nitropress) *Sodium nitroprusside and IV diazoxide are reserved for the management of hypertensive emergencies. Contraindications: severe HF, known inadequate cerebral perfusion (especially during neurosurgical procedures) F. Vasodilators Adverse Effects Hydralazine: dizziness, headache, tachycardia, edema, dyspnea, N/V/D, vitamin B6 deficiency, rash Sodium nitroprusside: hypotension, bradycardia, decreased platelet aggregation, rash G. Direct Renin Inhibitors Aliskirin (Tekturna) Blocks the RAS pathway at the point of activation. Inhibiting renin production prevents the downstream production of Ang II (potent vasoconstrictor) Adverse effects: N/V, severe hypotension, hyponatremia, hyperkalemia… Contraindicated in patients with DM taking ACEi or ARB Miscellaneous Antihypertensives Eplerenone (Inspra) Newer class of drugs called selective aldosterone blockers (remember RAAS?) Reduces BP by blocking the actions of aldosterone at its corresponding receptors in the kidney, heart, blood vessels, and brain Indications: routine treatment of hypertension and for post-MI HF Contraindicated if serum potassium levels are high (above 5.6 mEq/L) A Special Form of HTNTreatment of Pulmonary Hypertension Sildenafil and Tadalafil Commonly used for erectile dysfunction Used for pulmonary hypertension but with different trade names Sildenafil: Revatio* (Viagra for ED) Tadalafil: Adcirca* (Cialis for ED)

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