Problem 4.45 What is the probability that an electron in the ground state of hydro-gen will be found inside the nucleus?(a) First calculate the exact answer, assuming the wave function (Equation 4.80)is correct all the way down to r = 0. Let b be the radius of the nucleus.(b) Expand your result as a power series in the small number € = 2b/a, andshow that the lowest-order term is the cubic: P≈ (4/3)(b/a)³. This shouldbe a suitable approximation, provided that b

The radius of the nucleus is given as, b. Let b≈10-15 m and a≈0.5×10-10 m. TO DETERMINE: The…

Answered: Problem 4.45 What is the probability…

Similar questions

6.2 Let the "uniform" ensemble of energy E be defined as the ensemble of all systems of the given type with energy less than E. The equivalence between (6.29) and (6.27) means that we should obtain the same thermodynamic functions from the "uniform" ensemble of energy E as from the microcanonical ensemble of energy E. In particular, the internal energy is E in both ensembles. Explain why this seemingly paradoxical result is true.
2.5.2 (a) (b) From the results of Exercise 2.5.1, calculate the partial derivatives of f. 6, and with respect to r, e, and . With V given by 1a rsine ap är (greatest space rate of change), use the results of part (a) to calculate V-Vy. This is an alternate derivation of the Laplacian. Note. The derivatives of the left-hand V operate on the unit vectors of the right-hand V before the unit vectors are dotted together.
could you also explain to me how you come up with question A?
Problem 4.25 If electron, radius [4.138] 4πεmc2 What would be the velocity of a point on the "equator" in m /s if it were a classical solid sphere with a given angular momentum of (1/2) h? (The classical electron radius, re, is obtained by assuming that the mass of the electron can be attributed to the energy stored in its electric field with the help of Einstein's formula E = mc2). Does this model make sense? (In fact, the experimentally determined radius of the electron is much smaller than re, making this problem worse).
(a) Write down the wave functions for the three regions of the potential energy barrier (Figure 5.25) for E < U₁. You will need six coefficients in all. Use complex exponential notation. (b) Use the boundary conditions at x = 0 and at x = L to find four relationships among the six coeffi- cients. (Do not try to solve these relationships.) (c) Sup- pose particles are incident on the barrier from the left. Which coefficient should be set to zero? Why?
Math
Problem 4.38. Two magnetic systems in thermal contact Consider two isolated systems of noninteracting spins with NA energies are EA = -2µB and Eg = -2µB. = 4 and NB = 16. Their initial (a) What is the total number of microstates available to the composite system? (b) If the two systems are now allowed to exchange energy with one another, what is the probability that system A has energy EA? (c) What is the mean value of EA and its relative fluctuations? Calculate the analogous quantities for system B.