A non-normalized probability density for the position of an atom along the x-axis is given by, p(x) x {-(x + 1)(x-7) for -1Å ≤ x ≤ 7 Å otherwise 0 where x is in [Å] and p is in [Ź¹]. (a) Sketch the non-normalized probability density. Normalize the probability density. (b) (c) What is the probability that the atom is at a position x ≤ 1 Å? (d) What is the average position of the atom, (x)? The energy of the atom as function of position is given by E (x) = 2x², where x is in [Å] and E is in [eV]. (e) What is the average energy of the atom, (E)?
A non-normalized probability density for the position of an atom along the x-axis is given by, p(x) x {-(x + 1)(x-7) for -1Å ≤ x ≤ 7 Å otherwise 0 where x is in [Å] and p is in [Ź¹]. (a) Sketch the non-normalized probability density. Normalize the probability density. (b) (c) What is the probability that the atom is at a position x ≤ 1 Å? (d) What is the average position of the atom, (x)? The energy of the atom as function of position is given by E (x) = 2x², where x is in [Å] and E is in [eV]. (e) What is the average energy of the atom, (E)?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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![A non-normalized probability density for the position of an atom
along the x-axis is given by,
p(x) x (x + 1)(x-7) for -1Å ≤ x ≤ 7 Å
otherwise
0
where x is in [Å] and p is in [Å-¹].
(a) Sketch the non-normalized probability density.
(b) Normalize the probability density.
(c)
What is the probability that the atom is at a position
x ≤ 1 Å?
(d) What is the average position of the atom, (x)?
The energy of the atom as a function of position is given by
E(x) = 2x², where x is in [Å] and E is in [eV].
(e) What is the average energy of the atom, (E)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad5dfe01-69eb-4fdf-a353-20c354714f4c%2F108a1bcd-c3e5-4047-a1cd-5c9a8303238d%2Fltv7yc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A non-normalized probability density for the position of an atom
along the x-axis is given by,
p(x) x (x + 1)(x-7) for -1Å ≤ x ≤ 7 Å
otherwise
0
where x is in [Å] and p is in [Å-¹].
(a) Sketch the non-normalized probability density.
(b) Normalize the probability density.
(c)
What is the probability that the atom is at a position
x ≤ 1 Å?
(d) What is the average position of the atom, (x)?
The energy of the atom as a function of position is given by
E(x) = 2x², where x is in [Å] and E is in [eV].
(e) What is the average energy of the atom, (E)?
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