Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
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Chapter 36, Problem 53P
To determine
The probability of that the electron in the hydrogen ground state will be found in the radial-distance range
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6. An electron in hydrogen atom is in initial state
Þ(r, 0) = A(2410o + iÞ210 + 421–1 – 2ib211)
where wnim are the eigenfunctions of the hydrogen atom
a. Determine the constant A
b. What is the probability of finding the electron in the first excited state?
hw
= -
n2
c. Write the state Þ(r, t) at time t, using energy eigenvalues as En
d. Find the expectation value of L in the state Þ(r,t
e. Find the expectation values of Lx and Ly in the state (r, t
f. If measurement of Lz led to the value –ħ what will be results of measurement of
energy and the square of total orbital momentum immediately afterwards and
what are their probabilities?
Consider the Balmer series discussed in the book (and Prof. Scherer's lecture notes), where the
frequencies are given by:
x (3.29 × 1015 s-1)
n = 3,4,5, ..
v =
Let us focus only on the spectral lines and transitions corresponding to the Balmer series.
a) Suppose the Balmer series of hydrogen is studied using a Franck-Hertz experiment.
What is the threshold voltage required for n=3? How about n=4?
b) The Lyman Series frequencies are given by v = |1- x (3.29 x 1015 s-1). Describe
what is different about these two series of emission frequencies of photons from the
hydrogen atom? That is, what distinguishes one series from the other? (Hint: it may help
to think about the Bohr model interpretation of transitions.)
6. An electron in hydrogen atom is in initial state
p(r, 0) = A(2µ100 + ¡Þ210 + 4Þ21–1 – 2i4211)
where ynim are the eigenfunctions of the hydrogen atom
a. Determine the constant A
b. What is the probability of finding the electron in the first excited state?
c. Write the state p(r, t) at time t, using energy eigenvalues as En =
d. Find the expectation value of L in the state (r,t
e. Find the expectation values of Lx and Ly in the state (r, t
f. If measurement of L, led to the value -ħ what will be results of measurement of
energy and the square of total orbital momentum immediately afterwards and
what are their probabilities?
hw
n2
Chapter 36 Solutions
Essential University Physics (3rd Edition)
Ch. 36.1 - Prob. 36.1GICh. 36.2 - Prob. 36.2GICh. 36.3 - Prob. 36.3GICh. 36.4 - Prob. 36.4GICh. 36.5 - Prob. 36.5GICh. 36 - Prob. 1FTDCh. 36 - Prob. 2FTDCh. 36 - Prob. 3FTDCh. 36 - Prob. 4FTDCh. 36 - Prob. 5FTD
Ch. 36 - Prob. 6FTDCh. 36 - Prob. 7FTDCh. 36 - Prob. 8FTDCh. 36 - Prob. 9FTDCh. 36 - Prob. 10FTDCh. 36 - Prob. 11FTDCh. 36 - Prob. 12FTDCh. 36 - What distinguishes a Bose-Einstein condensate from...Ch. 36 - Prob. 14ECh. 36 - Prob. 15ECh. 36 - Prob. 16ECh. 36 - Prob. 17ECh. 36 - Prob. 18ECh. 36 - Prob. 19ECh. 36 - Prob. 20ECh. 36 - Prob. 21ECh. 36 - Prob. 22ECh. 36 - Prob. 23ECh. 36 - Prob. 24ECh. 36 - Prob. 25ECh. 36 - Prob. 26ECh. 36 - Prob. 27ECh. 36 - Prob. 28ECh. 36 - Prob. 29ECh. 36 - Prob. 30ECh. 36 - Prob. 31ECh. 36 - Prob. 32ECh. 36 - Prob. 33ECh. 36 - Prob. 34PCh. 36 - Prob. 35PCh. 36 - Prob. 36PCh. 36 - Prob. 37PCh. 36 - Prob. 38PCh. 36 - Prob. 39PCh. 36 - Prob. 40PCh. 36 - Prob. 41PCh. 36 - Prob. 42PCh. 36 - Prob. 43PCh. 36 - Prob. 44PCh. 36 - Prob. 45PCh. 36 - Prob. 46PCh. 36 - Prob. 47PCh. 36 - Prob. 48PCh. 36 - Prob. 49PCh. 36 - Prob. 50PCh. 36 - Prob. 51PCh. 36 - Prob. 52PCh. 36 - Prob. 53PCh. 36 - Prob. 54PCh. 36 - Prob. 55PCh. 36 - Prob. 56PCh. 36 - Prob. 57PCh. 36 - Prob. 58PCh. 36 - Prob. 59PCh. 36 - Prob. 60PCh. 36 - Prob. 61PCh. 36 - Prob. 62PCh. 36 - Prob. 63PCh. 36 - Prob. 64PCh. 36 - Prob. 65PCh. 36 - Prob. 66PCh. 36 - Prob. 67PCh. 36 - Prob. 68PCh. 36 - Prob. 69PCh. 36 - Prob. 70PCh. 36 - Prob. 71PCh. 36 - Prob. 72PCh. 36 - Prob. 73PCh. 36 - Prob. 74PCh. 36 - Prob. 75PCh. 36 - Prob. 76PPCh. 36 - Prob. 77PPCh. 36 - Prob. 78PPCh. 36 - Prob. 79PP
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