Tutorial 3

1. Tutorial 3 GEM2507 Physical Question from Everyday Life Vision, DNA, RNA and protein

2. Q1. In Young's double slit experiment, if we know that the distance from the center line to the first bright fringe is 5cm, what is the distance from the third to the fourth bright fringe? • d sin θ = m λ m = order of the bright fringe d (y1/L) = λ λ * L/d = y1 = 5 cm • y4 – y3 = (4 λ – 3 λ) * L /d = λ * L / d y4 – y3 = 5 cm So the distance from the third to the fourth bright fringe is 5 cm http://hypertextbook.com/physics/waves/introduction/

3. Additional notes Interference – Young’s Double-Slit Experiment The interference occurs because each point on the screen is not the same distance from both slits. Depending on the path length difference, the wave can interfere constructively (bright spot) or destructively (dark spot).

4. Slit separation = d; Distance on screen = x Angle of incidence = θ x = mλ bright = (m + ½)λ dark m= 0, 1, 2, … L sinθ~ tanθ~ θ~ x/L, small θ

5. Interference – Young’s Double-Slit Experiment We can use geometry to find the conditions for constructive and destructive interference: {Approx.: sinθ~ tanθ~ θ~ x/L, small θ}

6. Q2. Why would it be so that our eyes did not evolve such that we can see deep ultra-violet light? • It would damage our eyes because ultra-violet light carries high energy • Most organisms with colour vision are able to detect ultraviolet light. This high energy light can be damaging to receptor cells. With a few exceptions (snakes, placental mammals), most organisms avoid these effects by having absorbent oil droplets around their cone cells. • The alternative, developed by organisms that had lost these oil droplets in the course of evolution, is to make the lens impervious to UV light - this precludes the possibility of any UV light being detected, as it does not even reach the retina • If we had eyes that could see deep ultraviolet light, we would probably be single cell bacteria since we could not sustain a highly complex biological system that would be destroyed by ultraviolet light

7. 3. If vision is so advantageous, why wouldn’t plants have it? • If we say “advantageous”, we really should be more specific. Advantageous with respect to what? Certainly in the dark it won’t be of much use. Of course, plants need light so with respect to plants, darkness is not an issue. In order for vision to be useful, however, some means for reacting to what is seen is required. After all, there is no point in being able to see a predator if one cannot take any defensive action. • Furthermore, processing visual information requires some form of a brain. Hence, all in all, for vision to be useful, quite a few requirements must be fulfilled. For plants, it was apparently thus far not worth the resources to evolve vision but this does not mean that it will never happen 4. Why is it important for visual preprocessing to take place in the retina? • Visual information, is extraordinarily complex. Without preprocessing, too much data would need to be sent to the brain.

8. 5. Which elementary particle is associated with the microwaves in the eponymous kitchen appliance? • Microwaves are made up of photons. The wavelengths of microwave photons are much greater than those of visible light being in the order of centimeters. 6. Microwaves can cook food (and hence your brain as well). Yet we can see inside through a metal sheet with small holes. Why can the light pass through but apparently not the microwaves? Microwaves and visible light has different wavelength. The wavelength of visible light ranges from 400nm to 700 nm and the wavelength of microwave is in cm. The door of microwave has a glass panel with conduction perforated sheet whose holes a few mm in diameter. The holes is much larger that the wavelength of visible light. However, it is smaller than the wavelength of microwaves. Hence, visible light can easily pass through the hole but not microwaves.

9. 7. Why would it have been difficult for Fizeau to do his experiment inside a laboratory • Since the light is so fast, with ingenious setup, a fairly great distance between the light source and mirror is necessary. In Fizeau’s case, it is several kilometer away. Clearly that is much too far for laboratory

10. 8. Design a symmetric biconvex lens with a focal length of 2m Lens maker’s formula (textbook equation 13.9) For symmetric biconvex lens R1=R2, the above equation reduces to Sub in f = 2 m and nglass = 1.5, we get 0.12m 0.12m Taking d = 5mm, We get

11. 9. How many different polymers with a length of 5 monomers can be made if one has ten different types of monomers available? • If reading the sequence backward and forward is considered different (i.e. AAB ≠ BAA), then the number of different polymers N is given by the number of types to the power of the length of the sequence • N = (10)5 10. Speculate as to why herbivores can eat grass and properly digest it while human beings cannot Both human beings and herbivores can break α linkages since the bond is not that strong. β-linkages, however, are too strong for the mechanisms available to mammals to break. This is even so in the case of herbivores like cows and horses. Herbivore mammals solve this problem with the help of symbiotic bacteria that live in their digestive systems. The bacteria produce enzymes which break down the cellulose into simple sugars that are then used by the mammal as food

13. 11. What is the key difference between the DNA of a cyanobacterium and that of a human being? • When considering the molecular structure, the difference between human being and cyanobacterial DNA is nil. • However, there are big differences in how it is stored. In human beings, DNA is stored in the nucleus, while in bacteria it is in cytoplasm, since bacteria do not have a nucleus. Furthermore, DNA in bacteria can be in circular shape (forming plasmids) while human being DNA is linear and intricately packed. 12. Give an estimate of the atomic weight of a protein with an average length Average length of protein 300 amino acids Average molecular weight of an amino acid is about 135 Dalton

14. 13. Is there an enzyme that assists in the assembly of microtubules? 14. If there were only 12 different amino acids, how many different proteins with a length of 6 amino acids would be possible? If reading the sequence backward and forward is considered different (i.e. AAB ≠ BAA), then the number of different polymers N is given by • No. Microtubules have the remarkable ability to self-assemble. 15. If we proclaim that we need as many different possible proteins as there are atoms in the universe, then how long would a protein need to be? For simplicity assume that there are 20 different amino acids and that all proteins have equal length) • The number of atoms in the universe is 1078 • There are 20 amino acids used to synthesize a protein • Let define x as the length of the protein • 20x = 1078 x log 20 = 78 x = 59.95 ~ 60 • So, the length of the protein is 60 so that we can have as many different possible proteins as there are atoms in the universe

15. 16. Repeat the previous Exercise but allow the proteins to be of different lengths • If proteins allowed to be of different length, then the number of combinations of proteins can be synthesized up to a certain maximum length x is • Nprotein = 201 + 202 + … + 20x • = 20(20x – 1)/(20-1) = 20/19(20x – 1) • Nprotein = 1078 • 20/19(20x – 1) = 1078 • 20x = 19/20 x 1078 + 1 ~ 19/20 x 1078 • x log 20 = 78 + log 19/20 • x = 59.9 ~ 60 • So, we need the protein with a maximum length of 60

16. 17. If the average chicken egg has a weight of 58 g and its shell weighs about 6 g, how much protein does a chicken need to produce for its eggs in a year? (Chicken usually lay about 5 eggs a week) • According to page 323 in the textbook, about 11% of the weight of the egg yolk and white are protein. Hence if the egg weights 58 g and its shell 6g, the protein will be 11% of 52 g or about 5.7 g. • So if a chicken lays 5 eggs a week then in a year it will produce • Considering a chicken weighs about 2-3 kg, the amount of protein produced is usually more than half of its body weight

17. 18. What is the anti-codon corresponding to the amino acid lysine? • The codons associated with lysine are AAA and AAG. Hence the anti-codons can be UUU or UUC. 19. How is the energy for mRNA production supplied? When RNA polymerase transcribes mRNA, rather than using the nucleotides that make up mRNA, it uses versions of those nucleotides that have energy stored in them through extra phosphate groups. In employed nucleotides are ATP, UTP, CTP and GTP.