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
The time-independent
w (r) =
√
1
P =
wavefunction of the ground state of the hydrogen electron is a function of radial position r.
y
3/2
elas
In the equation, ao 0.0529 nm is the Bohr radius.
What is the probability P of finding the hydrogen electron within a spherical shell of inner radius 0.00600 nm and outer radius
0.0316 nm?
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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- .55 The radial probability density for the ground state of the hydrogen atom is a maximum whenr = a, where a is the Bohr ra- dius. Show that the average value of r, defined as P(r) r dr, has the value 1.5a. In this expression for ravgs each value of P(r) is weighted with the value of r at which it occurs. Note that the average value of r is greater than the value of r for which P(r) is a maximum.arrow_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
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