Models are particularly useful in relativity and quantum mechanics, where conditions are outside those normally encountered by humans. What is a model?
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- The lifetime of a muon is 2.20 ?s. If you measured its mass to be 105.7 MeV/c2, what would be the minimum (Heisenberg) uncertainty in this value? Sketch the situation, defining all of your variables5. The lifetime of a muon is 2.2 µs traversing the atmosphere at 0.98c (average) (a) What is the lifetime (Dt) of this unstable relativistic elementary particle in the rest reference frame of earth? (b) What is the minimum energy uncertainty range (DE) of this unstable particle?A thermometer system is composed of a sensor and a readout unit. the readout has an accuracy and resolution of +-0.7 C and +-0.62 C, respectively. The sensor has an accuracy of +-0.88 C and a hysteresis error of +-1.36 C. Estimate the design stage uncertainty in the temperature measurement for the readout and sensor combined.
- What is the meaning of a first order approximation?The average lifetime of a tau is about 2.9 ✕ 10−13 s. Estimate the minimum uncertainty in the energy of a tau. JGamma rays (?-rays) are high-energy photons. In a certain nuclear reaction, a ?-ray of energy 0.836 MeV (million electronvolts) is produced. Compute the frequency of such a photon. How do I enter 2.02*10^20 in the answer window?
- Scientists are conducting an experiment to determine if their hypothesis that a certain constant in the universe is 1.65. the uncertainties in the experiment result in a relative uncertainty of no more than 2%. After several experimental trials, the scientists obtained an average value of 1.7 for the constant. What can be said about the scientists hypothesis? Hint calculate the percent error and compare it to the relative uncertainty.6. The probability W(n) that an event characterized by a probability p occurs n times in N trials was shown by binomial distribution N! (N − n)! (c) From (b) show it reduces to W(n) = Consider the situation where the probability p is small and n << N (a) Show that (1-p)N-ne-p (b) Show that ≈Nn N! n!(N − n)!P” (1 − p)N-n W(n) = = where X = Np (d) From (c), show that properly normalized (e) Calculate the mean and variance \n n! e-tPhotons have a rest mass of zero. How can they have a non-zero momentum if this is the case? We know light slows down when moving through a medium. As it slows down, it gains mass. This allows it to have a momentum of more than zero. Classical momentum is to rest mass times velocity. Relativistic momentum is related to rest mass, velocity, and total energy. While the photon's rest mass is zero, its total energy is not. The laws of physics change when moving above 1% of the speed of light. This changes the definition of momentum. The rest mass of a photon is not zero in space, only when near the gravity of a planet like Earth.
- The photons that make up the cosmic microwave background were emitted about 380,000 years after the Big Bang. Today, 13.8billion years after the Big Bang, the wavelengths of these photons have been stretched by a factor of about 1100 since they were emitted because lengths in the expanding universe have increased by that same factor of about 1100. Consider a cubical region of empty space in today’s universe 1.00 m on a side, with a volume of 1.00 m3. What was the length s0 of each side and the volume V0 of this same cubical region 380,000 years after the Big Bang? s0 = ? m V0 = ? m^3 Today the average density of ordinary matter in the universe is about 2.4×10−27 kg/m3. What was the average density ?(rho)0 of ordinary matter at the time that the photons in the cosmic microwave background radiation were emitted? (rho)0 = ? kg/m^3Provide the answers in 90 minutes, and count as 2 questions if needed.As we have been slowly discovering more and more about the atoms we have encountered several different models of the atoms. All of these models have issues. One of the most common issues is the scale of the subatomic particles. Like the image below The proton in this model is too large. Given the following measurement, how many protons would need to set side-by-side to to equal the width of a hydrogen atom? The radius of a proton is 0.5636 fm (Femtometer). The diameter of a hydrogen atom is 7.5 Angstroms. must be written in Scientific noation.