Biophysics Lecture Notes PDF

by Don’t hesitate to contact me @ Mohamed Ahmed Sabet Hammam PHD Exp. Solid State Physics – Assiut University Email: [email protected] [email protected] 2 office hours/week - Bio413 – 3 floor...

by Don’t hesitate to contact me @ Mohamed Ahmed Sabet Hammam PHD Exp. Solid State Physics – Assiut University Email: [email protected] [email protected] 2 office hours/week - Bio413 – 3 floor rd Whatsapp group +201006773115  Biophysics Lecture timing 15 mins. Refreshment 70 mins. Explanation 15 mins. Questions and Answers Grades Class work + 15 Course Assessments quizzes You must exceed 60% Midterm 10 of the total course Practical class 10 points to pass this work course Practical final 5 Oral (with final) 10 Final 50 Sum 100 Quizzes Periodically all over the semester There may be two types: Written (using the 9 digits on the right on your ID no.) 3 0 2 0 5 9 6 7 1 Online (given link or QR-code scan) Let’s test this link: https://docs.google.com/forms/d/e/1FAIpQLSeVeW8eVONyR6fmVFiqbygMvIXS1fPsKAcUnFFMmO OXQMK9uA/viewform?usp=sf_link Practical 7 Experiments Labs are in biotechnology building : Bio201 Bio202 Bio203 Bio301 Bio302 Bio303 Evaluation in each week according to experiment results, student attitude in lab, pre- lab preparation (this represent 10 marks of the total 15 lab marks) You must confirm what is your next week experiment before leaving the lab Experiments are demonstrated in videos (Search for the YouTube channel named ‘Mohamed Sabet’) Final practical exam represents only 5 marks of total 15 lab marks How to study First of all, never translate the whole presentation into your mother tong language Just translate the unknown with your handwrite in the printed version to understand the concepts and the expressions use AI-tools like Chatgpt, Gemini, Claude, Microsoft copilot, Perplexity, and Socratic It’s never too late but your time don’t waste Help your colleagues, make a team work, it’s better for you before them  CHAPTER 1 Physics and Measurements Basic and Derived Quantities Systems of Units Dimensional Analysis Conversion of Units Vector & Scalar Quantities Basic and Derived Quantities The laws of physics are expressed in terms of basic quantities that require a clear definition and cannot be explained in terms of other physical quantities. Basic Quantities Length Mass Time Anyother mechanical quantities can be expressed by the combination of the basic quantities and are called derived quantities Derived Quantities Force Velocity Volume ……etc. Systems of Units C.G.S Units The C.G.S. system of units (Centimeter, Gram, Second system) is a French system. This system deals with only three fundamental units – the Centimeter, Gram and the Second for length, mass and time, respectively. F.P.S Units The F.P.S. system of units (Foot, Pound, Second system) is a British system. This system deals with only three fundamental units – the Foot, Pound and the Second for length, mass and time respectively. M.K.S Units The M.K.S. system of units (Meter, Kilogram, Second system) was set up by France. This system also deals with three fundamental units – the Meter, kilogram and the Second for length, mass and time, respectively. This system is also called the metric system of units and is closely related to C.G.S system of units.  Systems of Units SI Units The measurement system which is internationally accepted now is suggested by the Eleventh general conference of weights and Measures in 1960 - France and is known as SI units of measurement. There are seven basic or fundamental units and three supplementary units. The basic units are The supplementary units are the radian (rad) for angle, the steradian (sr) for solid angle, Mechanical the meter (m) for length, Quantities the kilogram (kg) for mass, the becquerel (Bq) for radioactivity. the second (s) for time, Non-Mechanical the Kelvin (K) for temperature, Quantities the ampere (A) for electric current, the candela (cd) for luminous intensity and the mole (mol) for the amount of substance. SI System Standards The International committee established a set of standards for the three basic quantities as follows: Length Standard of length is based on speed of light in vacuum. Meter (m): distance travelled by light in vacuum during a time of 𝐿 (𝑚) 𝑐= = 299 792 458 (𝑚/𝑠) 𝑡 (𝑠) 1 𝑚 1 𝑡 𝑠 = 𝑚 ≅ 8 𝑠 299 792 458 3 × 10 𝑠 Mass Standard of mass is based on the mass of an alloy. Kilogram (kg): mass of a specific Pt-Ir alloy cylinder. Because Pt-Ir alloy is very stable against corrosion or oxidation. Time Standard of time is based on the atomic clock of Cs133 atom. Second (s): obtained by the characteristic frequency (period of vibration ) of radiation from the Cs133 atom. The periodic time of the Cs133 radiation is 1 𝑇 = 𝑠 9192631770 T Time 1 𝑠 = 9 192 631 770 × 𝑇 Dimensional Analysis Dimension denotes the physical nature of a quantity and is described using the basic quantities like: Length; L - Mass; M - Time; T It doesn’t take into account the proportionality constants in equations or the system of units. We denote it by placing the physical quantity in square brackets. Dimensions of some physics quantities: Area [A] = L.L = L 2 Check out this video https://youtu.be/ntKsDKAJlUc Volume [V] = L.L.L = L 3 Click on the link then click on browse YouTube Velocity [ν] = L / T = LT-1 Acceleration [a] = [v/t] = L / T2 = LT-2 Force [F] = [m]. [a] = M LT -2 Momentum [P] = [m]. [ν] = MLT -1 Kinetic Energy 2 -1 2 [K.E] = [1/2].[m]. [ν ] = M((LT ) ) = ML T 2 -2 Potential Energy [P.E] = [m]. [g]. [h] = M(LT-2) L = ML2T-2 Note: [K.E] = [P.E] Pressure [P] = [F/A] = M LT-2/L2 = M L-1T-2 Density [ρ] = [m/V] = ML -3 Problem 𝑀𝑚 Newton’s Law of universal gravitation is 𝐹 = 𝐺 2 𝑟 where F is the force of gravity and M, m are masses; and r is a length. What are the units of G in the SI units? Solution 𝑀𝑚 𝐹=𝐺 2 𝑟 2 M m 𝐹𝑟 𝐺= 𝑀𝑚 𝑀𝐿𝑇 𝐿−2 2 r [𝐺] = 2 𝑀 𝐿 3 𝐺 = 2 𝑀𝑇 The unit of G in the SI units are: 3 m /kg.s 2 Conversion of Units and Prefixes Prefixes is used to multiply or divide the base units by powers of 10. For example, the prefix "kilo" means 1000, so one kilometer (km) is equal to 1000 meters. g g g Quiz Example 2 2 What is the area of 2 in paper in m ? Answer 1 𝑖𝑛 = 2.54 𝑐𝑚 −2 1 𝑖𝑛 = 2.54 × 10 𝑚 2 −2 −2 2 −4 1 𝑖𝑛 = 2.54 × 10 × 2.54 × 10 𝑚 = 6.45 × 10 𝑚 2 Then 2 𝑖𝑛 2 = 2 × 6.45 × −4 10 𝑚 2 = 12.9 × −4 10 𝑚 2 Quiz Example The mass of a solid cube is 856 g, and each edge has a length of 5.35 cm. Determine the density 𝝆 of the cube in basic SI units? Answer 1𝑔 = −3 10 𝑘𝑔 1𝑐𝑚 = 10 𝑚−2 𝑉𝑜𝑙𝑢𝑚𝑒 = 𝐿 = 5.35 × 10 3 −2 3 −4 = 1.53 × 10 𝑚 3 −3 𝑀𝑎𝑠𝑠 = 856 × 10 = 0.856 𝑘𝑔 3 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 = 5.59 × 10 𝑘𝑔 /𝑚 3 Vector & Scalar Quantities A scalar quantity is completely specified by a single value with an appropriate unit and has no direction. A vector quantity is completely described by a number and appropriate units plus a direction. A particle travels from A to B along the path shown by the broken line. This is the distance traveled and is a scalar. The displacement is the solid line from A to B and is independent of the path taken between the two points. The displacement is a vector. Vector Properties The vector magnitude has physical units (m/sec., N, 2 m/sec. ,…) The magnitude is always a positive number. The direction is an angle relative to a reference line (positive x-axis direction). Vectors could be written as 𝐴 or in a bold print A While the magnitude of a vector, is written in italic letter as A or 𝐴 Distance Adds Up Vector Properties  Two vectors 𝐴 and 𝐵 are equal if they have the same magnitude and the same direction (i.e. A = B and they point along parallel lines).  All of the vectors shown are equal.  Vector can be moved to a position parallel to itself Vector Components Components are the projections of a vector along the x- and y-axes. The magnitude of the x-component of a vector is the projection along the x-axis. 𝑨𝒙 = 𝑨 𝒄𝒐𝒔 𝜽 The magnitude of the y-component of a vector is the projection along the y-axis. 𝑨𝒚 = 𝑨 𝒔𝒊𝒏 𝜽 This assumes the angle θ is measured with respect to the x-axis. The magnitude A and the direction θ of any vector 𝐴 could be found using the magnitude of the components Ax and Ay. 𝟐 𝟐 𝑨= 𝑨𝒙 + 𝑨𝒚 −𝟏 𝑨𝒚 𝜽 = 𝒕𝒂𝒏 𝑨𝒙 The components could be positive or negative, have the same units as the original vector and their signs depend on the angle. Vector Components A unit vector is a dimensionless vector with a magnitude of exactly 1 and are only used to specify the direction. 𝒊 = 𝒋 = 𝒌 =𝟏 The complete vector (in three dimensions) can be expressed as: 𝐴 = 𝐴𝑥 𝑖 + 𝐴𝑦 𝑗 + 𝐴𝑧 𝑘 The vector form in two dimensions: 𝐴 = 𝐴𝑥 𝑖 + 𝐴 𝑦 𝑗 Adding Vectors We could add or subtract two or more vectors algebraically by using the complete vector form described by the unit vectors, as follows: 𝑅 =𝐴+𝐵 𝑅 = 𝐴𝑥 𝑖 + 𝐴𝑦 𝑗 + 𝐵𝑥 𝑖 + 𝐵𝑦 𝑗 𝑅 = 𝐴𝑥 + 𝐵𝑥 𝑖 + 𝐴𝑦 + 𝐵𝑦 𝑗 𝑅 = 𝑅𝑥 𝑖 + 𝑅𝑦 𝑗 Where 𝑅𝑥 = 𝐴𝑥 + 𝐵𝑥 and 𝑅𝑦 = 𝐴𝑦 + 𝐵𝑦 are the components of 𝑅. While the magnitude R and the direction θ are given by 2 2 𝑅= 𝑅𝑥 + 𝑅𝑦 −1 𝑅𝑦 𝜃= 𝑡𝑎𝑛 𝑅𝑥 Adding Vectors Example Given the vectors A = 2.00 i +6.00 j and B = 3.00 i - 2.00 j, C = A + B and the vector difference D = A - B. Calculate C and D, first in terms of unit vectors and then in terms of magnitudes and angles. Answer 𝑪 = 𝑨 + 𝑩 𝑪 = 2.00 𝒊 + 6.00 𝒋 + 3.00 𝒊 − 2.00 𝒋 𝑪=5𝒊 + 4𝒋 Then the magnitude is 2 2 𝑪 = 5 + 4 = 25 + 16 = 6.4 In addition, the direction is −1 4 𝜃𝐶 = 𝑡𝑎𝑛 = 38.7° 5 Adding Vectors On the other hand, 𝑫 = 𝑨− 𝑩 𝑫 = 2.00 𝒊 + 6.00 𝒋 − 3.00 𝒊 − 2.00 𝒋 𝑫=−𝒊 + 8𝒋 Then the magnitude is 𝑫 = −1 2 +8 2 = 1 + 64 = 8.06 In addition, the direction is −1 8 𝜃𝐷 = 𝑡𝑎𝑛 = 97.125° −1 Note while calculations: If the x-component of any vector is a negative value, then add 180° to the angle calculated using the calculator to correct the sign error. Vector Multiplication The multiplication of a vector by a scalar quantity produce a vector product that changes its magnitude. It reverses its direction if the scalar quantity is negative. For any scalar quantity 𝑎 and a vector 𝑅 : 𝑎. 𝑅 = 𝑎. 𝑅𝑥 𝑖 + 𝑅𝑦 𝑗 + 𝑅𝑧 𝑘 = 𝑎. 𝑅𝑥 𝑖 + 𝑎. 𝑅𝑦 𝑗 + 𝑎. 𝑅𝑧 𝑘 The multiplication of two vectors may be done by two methods: The scalar (dot) product that produces a scalar quantity The vector product that produces a vector quantity Vector Multiplication The scalar (dot) product If the components of the two vectors (Ax, Ay, Az for vector 𝐴 and Bx, By, Bz for vector 𝐵) are given, the scalar product is given by 𝐴. 𝐵 = 𝐴𝑥 𝐵𝑥 + 𝐴𝑦 𝐵𝑦 + 𝐴𝑧 𝐵𝑧 If the magnitudes of the two vectors 𝐴 and 𝐵 (A, B) and the angle between the two vectors 𝐴 and 𝐵 are given, the scalar product is given by 𝐴. 𝐵 = 𝐴𝐵 cos 𝜃 Where 𝜃 is the angle between 𝐴 and 𝐵 Vector Multiplication The vector product is determined using the next determent 𝑖 𝑗 𝑘 𝐴 × 𝐵 = 𝐴𝑥 𝐴 𝑦 𝐴𝑧 𝐵𝑥 𝐵𝑦 𝐵𝑧 = 𝐴𝑦 𝐵𝑧 − 𝐴𝑧 𝐵𝑦 𝑖 − 𝐴𝑥 𝐵𝑧 − 𝐴𝑧 𝐵𝑥 𝑗 + 𝐴𝑥 𝐵𝑦 − 𝐴𝑦 𝐵𝑥 𝑘 Where the components of the two vectors 𝐴 and 𝐵 are Ax, Ay, Az for vector 𝐴 and Bx, By, Bz for vector 𝐵 The magnitude of the vector product is obtained by 𝐴 × 𝐵 = 𝐴𝐵 sin 𝜃 Where 𝜃 is the angle between 𝐴 and 𝐵 Vector Multiplication Using the right hand rule to find the direction of the vector product Vector Multiplication Example Another answer Vector Multiplication Example