-15 61. The radius of a proton is about Ro 10 m. The probability that the...
Calculate the probability of an electron in the ground state of the hydrogen atom being inside the region of the proton. (For purposes of calculation, use a proton radius r = 0.960 x 105 m. Hint: Note that r << an.) X
Calculate the radial probability density P(r) for the hydrogen atom in its ground state at (a)r=0 and (b) r= 2.75a, where a is the Bohr radius. (a) Numberto (b) Number 13.65E10 unitesimm-1 units nm-1
The nucleus of a hydrogen atom is a single proton, which has a radius of about 1.1 10-15 m. The single electron in a hydrogen atom normally orbits the nucleus at a distance of 5.5 10-11 m. What is the ratio of the density of the hydrogen nucleus to the density of the complete hydrogen atom?
1) (60 points) The ground state of the hydrogen atom: In three dimensions, the radial part of the Schrodinger equation appropriate for the ground state of the hydrogen atom is given by: ke2 -ħ2 d2 (rR) = E(rR) 2me dr2 where R(r) is a function of r. Here, since we have no angular momentum in the ground state the angular-momentum quantum number /=0. (a) Show that the function R(r) = Ae-Br satisfies the radial Schrodinger equation, and determine the values...
B.2 [10p]. Consider the ground state of the Hydrogen atom. Compute the probability of finding the electron in a spherical region of radius 1 Ă around the proton. Uground (r, 0,0) = - e-r/ro ћc with ro = 0 am.c2 VT23/2 er/ (1.5)
Problem 10 (Problem 2.24 in textbook) The wavefunction for the electron in a hydrogen atom in its ground state (the 1s state for which n 0, l-0, and m-0) is spherically symmetric as shown in Fig. 2.14. For this state the wavefunction is real and is given by exp-r/ao h2Eo 5.29 x 10-11 m. This quantity is the radius of the first Bohr orbit for hydrogen (see next chapter). Because of the spherical symmetry of ịpo, dV in Eq. (2.56)...
If the radius of a nucleus is given by R = Ro A 1/3 where Ro = 1.2X10-15 m, calculate the density of a nucleus that has A = 233. Assume the mass of the nucleon (proton or neutron) = 1.67x10-27 kg.
* *SHOW YOUR WORK & INCLUDE CORRECT UNITS for FULL CREDIT* e probability function P(r) associated from the radial wave function for an electron in the first excited Hydrogen ( 2p state n = 2 ) is given by: 4 P(r) = where ri-0.53x10""m (Bohr radius) a) Determine the three critical points associated with this radial probability function by evaluating: dP _=0 dr Regarding maxima and minima, deduce the most probable and least probable radial locations for the electron in...
The nucleus of the hydrogen atom has a radius of about 1.0 × 10-15 m. The electron is at a distance of about 5.29 × 10-11 m from the nucleus. Assuming the hydrogen atom is a sphere with a radius of 5.29 × 10-11 m, find (a) the volume of the atom, (b) the volume of the nucleus, and (c) the percentage of the volume of the atom that is occupied by the nucleus.
2. [Total: 18 pts] In this problem you will analyze the probability that an electron in the ground state of hydrogen will be found inside the nucleus. a) [6 pts) Let b be the radius of nucleus, first calculate the exact answer using the ground state wave function. b) [6 pts Expand your result from part a) as a power series in the small number e = 2b/a, and show that the lowest-order term is P = (4/3)(b/a)'. This should...