a- Find the radius r₁ of the electron in the ground state orbit of doubly ionized potassium which has an atomic number Z = 19.
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- In Figure 23-29, a proton is a distance d/2 directly above the center of a square of side d. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge d.)A particle moves along line segments from the origin to the points (2, 0, 0), (2, 5, 1), (0, 5, 1), and back to the origin under the influence of the force field F(x, y, z) = z2i+ 3xyj + 3y2k. Use Stokes' Theorem to find the work done.A photon moving in the +x-direction, scatters off a free stationary electron. The wavelength of the incident photon is 0.0310 nm. After the collision, the electron moves at an angle a below the +x- axis, while the photon moves at an angle = 81.3° above the +x-axis. (For the purpose of this exercise, assume that the electron is traveling slow enough that the non-relativistic relationship between momentum and velocity can be used.) (a) What is the angle a (in degrees)? 47.21 X What is the shift in wavelength of the photon due to the scattering? How can you use momentum conservation in the horizontal and vertical directions to determine the angle? counterclockwise from the +x-axis (b) Determine the speed of the electron (h m/s). m/s
- 3 Charged Closed Wire Consider a thin closed wire with the radius R localized at the origin on the xy-plane, which is charged uniformly with the total charge Q. (i) What is the charge density p in this problem? (ii) Calculate the electric field along the z axis? (Hint: First, consider an infinitessimal piece of the charge.)Q5: Consider the formula B = 2ol J’ds:e 4 r and give an explanation of the magnetic field unit ?A compound contains 0.25 moles of element X and 0.50 moles of element Y. Determine its empirical formula. OXY3 ©XY, OX3Y OX3Y2 OX2Y
- Consider the radiation with the following wavelengths: 1. 600 nm II. 200 nm III. 1200 nm Arrange by: LOWEST energy LOWEST frequency HIGHEST energy_ ergy_||| A. I, I, III B. II, II, I C. III, III, I D. III, II, II E. II, II, III 2011.5 The overlap integral S for the H₂+ molecule can be eval- uated as R R2 -Rlao S = 1 + + ao Заг Plot this as a function of R/ao. At what value of R is it a maxi- mum? At what value of R is it a minimum? What is the value of 106 pm? S at the equilibrium separation, R =1. Rank the rate of the SN2 reaction with NaOCH3 as the nucleophile. Br Br Br Br
- What is the separation between two slits for which 580 nm light has its first minimum at an angle of 28.4°?(4) Air at 100kPa, 295K and moving at m 710 is decelerated isentropically to S m 250. Determine the final static S temperature and static pressure. [515 K, 702kPa]Question 3 The Black-Scholes model is a time series (X₂) that follows the dynamics X₁ = X₁-1*exp(μ+0€) where μ, >0 and () is a time series of independent and identically distributed standard Gaussian random variables. Note that E(exp(μ+σt)) = "¹+0² (i) Show that the log-returns of this process X, form a white noise process (ii) Suppose E(X) = 0. Compute E(X₂). Determine if the variance of X, is falling, remains constant or is growing in t.