Planck's Constant

Planck's Constant

• Symbolized as "h".
• Has a value of $6.626 \times 10^{-34} J \cdot s$
• Is a fundamental constant in quantum mechanics.
• Relates a photon's energy to its frequency.
• Describes the quantized nature of energy.
• Important for understanding the behavior of particles at the atomic and subatomic levels.

Key Concepts

• Energy is quantized, existing in discrete packets called quanta, not continuously.
• Photon energy (E) is proportional to its frequency (v): $E = h \cdot v$.

Applications

• Explains blackbody radiation, the spectrum of light emitted by heated objects.
• Describes the photoelectric effect, where light shining on a material causes electron emission.
• Predicts discrete wavelengths of light emitted by atoms, which is known as atomic spectra.

Significance

• Bridges classical physics and quantum mechanics.
• Provides a foundation for understanding the quantum world.

Lecture 15: The Chemical Senses

• Chemosenses include gustation (taste) and olfaction (smell).

Importance of Chemical Senses

• They contribute to pleasure and evoke memories.
• They influence social behavior.
• When combined, they produce the sensation of "flavor".
• They warn of harmful substances.

Taste

• Gustation is the "gatekeeper" of the body.

Basic Tastes

• Consist of sweet, sour, salty, bitter, and umami.

Flavor Complexity

• Retronasal olfaction occurs when olfactory receptors are activated by sniffing and chewing.
• Flavor is influenced by mouth feel, temperature, and pain.

The Tongue

• Papillae are taste receptor-containing structures.
• Four types of papillae exist: filiform, fungiform, foliate, and circumvallate.

Papillae Types

• Filiform papillae are cone-shaped, located all over the tongue, and do not contain taste buds.
• Fungiform papillae are mushroom-shaped, found on the tip and sides of the tongue, and contain an average of 6 taste buds.
• Foliate papillae are folds along the back sides of the tongue and have hundreds of taste buds.
• Circumvallate papillae are flat mounds at the back of the tongue, containing hundreds of taste buds.

Taste Buds

• Contain 50-100 taste receptor cells, which have receptors for particular molecules.
• Taste cells have receptors at their tips.
• Molecule binding causes electrical signals.
• Signals travel up the taste nerve.

Taste Transduction

• Molecules in food bind to receptors on taste cells, potentially opening ion channels.
• This causes a change in membrane potential called a receptor potential.
• Signals travel up the taste nerve, transmitting gustatory information to the brain.

Taste Pathways

• Taste receptor cells project to cranial nerves, then to the medulla, and finally to the thalamus.
• Two main pathways diverge in the thalamus, leading to the insula and orbitofrontal cortex.

Neural Coding for Taste

• Population coding involves patterns of activity across many neurons.
• Taste qualities are determined by activity across many different taste neurons.
• Evidence for population coding comes from across-fiber patterns found in monkey taste nerves.
• Labeled-line coding suggests each taste neuron responds to only one taste quality.

Genetic Variation in Taste

• The Perception of taste is impacted by age and experience
• Genetic variation exists in receptors, such as PTC/PROP.
• Supertasters, tasters, and nontasters exist.

Olfaction

• Olfaction is the sense of smell used to detect odors.
• It serves as a warning signal and facilitates communication through pheromones, contributing to flavor perception.

Olfactory Pathway

• Odor molecules travel to olfactory receptor neurons (ORNs) in the olfactory epithelium.
• From there, signals proceed to the olfactory bulb and then to the olfactory cortex.

Nose to Brain

• Odorant molecules travel through the nose to the olfactory epithelium.
• The nasal passage includes olfactory receptor neurons (ORNs), supporting cells, and basal cells.

Olfactory Receptor Neurons (ORNs)

• Contain cilia with olfactory receptors.
• Humans have about 350 different olfactory receptors.
• ORNs respond to a range of odorants.
• Each neuron has one type of receptor.
• Olfactory receptors are proteins that traverse the cell membrane seven times.

Olfactory Transduction

• An odorant binds to a receptor, activating a G-protein.
• The activated G-protein activates an enzyme, leading to the formation of cAMP.
• cAMP opens ion channels, allowing Na+ and Ca2+ to enter the cell, causing depolarization.

Olfactory Pathway

• Olfactory receptor neurons (ORNs) project to the olfactory bulb.
• ORNs with a particular receptor type project to one or two glomeruli in the olfactory bulb.
• The olfactory bulb projects to the olfactory cortex, bypassing the thalamus.

Population Coding in Olfaction

• Patterns of ORN activation code odor.
• Specific glomeruli are activated by different odors, resulting in a combinatorial code.

Chemotopic Map

• Molecules with similar structures activate similar areas of the olfactory bulb.

Adaptation in Olfaction

• Receptor adaptation occurs when olfactory receptors stop responding to an odorant.
• Cross-adaptation is when exposure to one odorant reduces sensitivity to other odorants.
• Cognitive habituation happens when one can’t detect an odor at all after repeated exposure.

Pheromones

• Pheromones are chemical signals released by an individual that affect the physiology and behavior of others.
• They are used for communication, including functions like territorial marking, mate selection, and alarm signals.

Possible Human Pheromones

• Most mammals have a vomeronasal organ (VNO), but humans do not.
• Androstadienone, a steroid in male sweat, makes women rate faces more attractive after exposure.

Fisica: Vectores (Vectors)

Vector Summation

Algebraic Method

• Vectors can be described by their components.
• $\vec{A} = A_x\hat{i} + A_y\hat{j}$
• $A_x$ can be defined as $A\cos(\theta)$
• $A_y$ can be defined as $A\sin(\theta)$

Example

Given the following vectors:

• $\vec{A} = 25m, 30^\circ$
• $\vec{B} = 40m, 120^\circ$
• The resultant vector $\vec{R}$ is the sum of $\vec{A}$ and $\vec{B}$.
• $\vec{R} = \vec{A} + \vec{B}$

Calculate Component x

• $A_x = 25\cos(30^\circ) = 21.65m$
• $B_x = 40\cos(120^\circ) = -20m$
• $R_x = A_x + B_x = 21.65m - 20m = 1.65m$

Calculate Component y

• $A_y = 25\sin(30^\circ) = 12.5m$
• $B_y = 40\sin(120^\circ) = 34.64m$
• $R_y = A_y + B_y = 12.5m + 34.64m = 47.14m$

Calculate Resultant vector

• $\vec{R} = 1.65\hat{i} + 47.14\hat{j}$
• $R = \sqrt{R_x^2 + R_y^2} = \sqrt{1.65^2 + 47.14^2} = 47.17m$
• $\theta = \tan^{-1}(\frac{R_y}{R_x}) = \tan^{-1}(\frac{47.14}{1.65}) = 88^\circ$
• $\vec{R} = 47.17m, 88^\circ$

Bernoulli Effect

• As fluid (liquid or gas) speed increases, internal pressure decreases.
• Faster-moving fluids exert less pressure than slower-moving ones.

Key Points

• The conservation of energy and the Bernoulli effect imply that a fluid's total mechanical energy, including pressure and kinetic energy, remains constant.
• There exists an inverse relationship between fluid pressure and speed.
• As fluid flows through a constricted area, its speed increases, and the pressure it exerts decreases.

Applications

• Airplane wings are designed with a curved upper surface; air travels faster with lower pressure above and slower with higher pressure below, producing lift.
• Atomizers/sprayers: High-speed air over a tube of liquid creates low pressure, drawing the liquid up and atomizing it.
• Venturi meters measure flow rate by measuring pressure differences between wider and constricted pipe sections.

Mathematical Representation

• The Bernoulli equation relates pressure, speed, and height: $P + (1/2) \rho v^2 + \rho gh = constant$
  • $P$ is the pressure of the fluid.
  • $\rho$ is the density of the fluid.
  • $v$ is the speed of the fluid.
  • $g$ is the acceleration due to gravity.
  • $h$ is the height of the fluid above a reference point.

Limitations

• Most accurate for incompressible fluids at low speeds. Less accurate for gases with speeds.
• Assumes the fluid is non-viscous. Viscosity can affect flow and pressure, especially in narrow channels or high flow rates.
• Based on the assumption of laminar flow. Turbulent flows are inconsistent.
• Assumes no heat transfer. Significant heat transfer alters the relationship between pressure and speed.