EBK PHYSICS FOR SCIENTISTS & ENGINEERS
5th Edition
ISBN: 9780134296074
Author: GIANCOLI
Publisher: VST
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Chapter 39, Problem 2Q
To determine
An explanation for the probability density to be maximum at the centre of the H atom in the ground state but the radial probability density to be zero at this point.
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Determine the integral
| P(r) dr
for the radial probability density for the ground state of the hydrogen atom
4
P(r) =
- r²e-2rla
a³
O 1
O-1
O 0.5
Suppose you measure the angular momentum in the z-direction L, for an /= 2 hydrogen atom in the state | >
2 >
|0 > +i/ |2 >. The eigenvalues of
%3D
V10
10
Lz are – 2h, -ħ, 0, ħ, 2ħfor the eigenvectors | – 2 >, |– 1>, |0 >, |1 >, |2 >, respectively. What is AL,?
V31
10
7
19
25
H-atom. The wave function of one of the electrons in the 2p orbital is given by (ignoring spin)
r
2,1,0 (1,0,0)=
- 7 exp(-270) c
ao
1
|32πα
cose
Where do is the Bohr radius. In the Bohr model, the radius of the electron orbit is given by m=2 =
n²ao = 4ao. The probability that the electron can be found at some radius between r and r + dr is
given by
2π
P(r) dr = √2
= √ ₁²ª d$ S ²
What is the expectation value of the distance of the electron from the nucleus (r)?
Clue: expected value is computed by (r) = forP(r) dr then do integration by parts
do sin 0 de | Yn.l.m² (r, $,0)|²r² dr
Chapter 39 Solutions
EBK PHYSICS FOR SCIENTISTS & ENGINEERS
Ch. 39 - Prob. 2QCh. 39 - Prob. 3QCh. 39 - Prob. 4QCh. 39 - Prob. 5QCh. 39 - Prob. 6QCh. 39 - Prob. 7QCh. 39 - On what factors does the periodicity of the...Ch. 39 - Prob. 9PCh. 39 - Prob. 10PCh. 39 - Prob. 11P
Ch. 39 - Prob. 12PCh. 39 - Prob. 13PCh. 39 - Prob. 14PCh. 39 - Prob. 15PCh. 39 - Prob. 16PCh. 39 - Prob. 17PCh. 39 - Prob. 18PCh. 39 - Prob. 19PCh. 39 - Prob. 20PCh. 39 - Prob. 21PCh. 39 - Prob. 22PCh. 39 - Prob. 23PCh. 39 - Prob. 24PCh. 39 - Prob. 25PCh. 39 - Prob. 26PCh. 39 - Prob. 27PCh. 39 - Prob. 34PCh. 39 - Prob. 35PCh. 39 - Prob. 36PCh. 39 - Prob. 37PCh. 39 - Prob. 40PCh. 39 - Prob. 41PCh. 39 - Prob. 42PCh. 39 - Prob. 43PCh. 39 - Prob. 44PCh. 39 - Prob. 45PCh. 39 - Prob. 46P
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- (a) How much energy is required to cause an electron in hydrogen to move from the n = 2 state to the n = 5 state? in J(b) Suppose the atom gains this energy through collisions among hydrogen atoms at a high temperature. At what temperature would the average atomic kinetic energy 3/2 * kBT be great enough to excite the electron? Here kB is Boltzmann's constant. in Karrow_forward(a) How much energy is required to cause an electron in hydrogen to move from the n = 2 state to the n = 5 state?in J(b) Suppose the atom gains this energy through collisions among hydrogen atoms at a high temperature. At what temperature would the average atomic kinetic energy 3/2 * kBT be great enough to excite the electron? Here kB is Boltzmann's constant. in Karrow_forward(a) The L→ K transition of an X-ray tube containing a molybdenum (Z = 42) target occurs at a wavelength of 0.0724 nm. Use this information to estimate the screening parameter of the K-shell electrons in molybdenum. [Osmania University]arrow_forward
- The radial part of the Schrödinger equation for the hydrogen atom д ħ ² l ( l + 1 ) Ze² 240² or (2² (1) 2μr dr ər R(r) = ER(r) 2μr² + -R(r) – Απε has eigenvalues that depend on only the principal quantum number, n. True Falsearrow_forwardConsider the n = 4 states of hydrogen. (a) What is the maximum magnitude L of the orbital angular momentum? (b) What is the maximum value of Lz? (c) What is the minimum angle between L S and the z-axis? Give your answers to parts (a) and (b) in terms of h.arrow_forwardCompute the intrinsic line-width (Δλ) of the Lyman α line (corresponding to the n=2 to n=1) transition for the Hydrogen atom. You may assume that the electron remains in the excited state for a time of the order of 10^−8s. The line-width may be computed using:ΔE=(hc/λ^2)Δλarrow_forward
- (a) List all possible sets of quantum numbers (n, l, ml , ms) for the n = 3 shell, and determine the number of electrons that can be in the shell and each of its subshells. (b) Show that the number of electrons in the shell equals 2n2 and that the number in each subshell is 2(2l + 1) .arrow_forwardAt what radius in the H atom does the radial distribution function of the ground state have (i) 50 per cent, (ii) 75 per cent of its maximum value?arrow_forwardFor a hydrogen atom in an excited state with principal quantum number n, what is the smallest angle that the orbital angular momentum vector can make with respect to the z-axis.arrow_forward
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