Question 2 The ammonia molecule, NH3, has a trigonal pyramidal molecular shape. Its Cartesian coordinates are given below. Atom X/A Y/A Z/Å N 0.000000 0.000000 0.096922 H 0.000000 0.969142 -0.226150 H -0.839302 -0.484571 -0.226150 H 0.839302 -0.484571 -0.226150 a) Calculate the length of the N-H bond. (6 marks) b) Calculate the H-N-H bond angle. c) (6 marks) The overall dipole moment of NH3 is 1.42 D. Calculate the dipole moment of an individual N-H bond. (6 marks) d) In two-dimensional space, the rotation matrix that transforms the coordinates (x,y) to (x2,y2) is given by (x2,y2) R(0) = [cos-sine], 0 (x₁₁) where | = R()] x Fig. 1. Transformation of (x,y) to (x2,y2) by rotation about angle 0. A sketch illustrating the angle 0 and the coordinates (x,y) and (x2,y2) is given in Fig. 1. Show that the three H atoms in NH3 are spaced 120° apart. (7 marks) 3
Question 2 The ammonia molecule, NH3, has a trigonal pyramidal molecular shape. Its Cartesian coordinates are given below. Atom X/A Y/A Z/Å N 0.000000 0.000000 0.096922 H 0.000000 0.969142 -0.226150 H -0.839302 -0.484571 -0.226150 H 0.839302 -0.484571 -0.226150 a) Calculate the length of the N-H bond. (6 marks) b) Calculate the H-N-H bond angle. c) (6 marks) The overall dipole moment of NH3 is 1.42 D. Calculate the dipole moment of an individual N-H bond. (6 marks) d) In two-dimensional space, the rotation matrix that transforms the coordinates (x,y) to (x2,y2) is given by (x2,y2) R(0) = [cos-sine], 0 (x₁₁) where | = R()] x Fig. 1. Transformation of (x,y) to (x2,y2) by rotation about angle 0. A sketch illustrating the angle 0 and the coordinates (x,y) and (x2,y2) is given in Fig. 1. Show that the three H atoms in NH3 are spaced 120° apart. (7 marks) 3
Calculus: Early Transcendentals
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Chapter1: Functions And Models
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Whole of question 2
ans for part c us 1.5D
![Question 2
The ammonia molecule, NH3, has a trigonal pyramidal molecular shape. Its Cartesian
coordinates are given below.
Atom
X/A
Y/A
Z/Å
N
0.000000
0.000000
0.096922
H
0.000000
0.969142
-0.226150
H
-0.839302
-0.484571
-0.226150
H
0.839302
-0.484571
-0.226150
a)
Calculate the length of the N-H bond.
(6 marks)
b)
Calculate the H-N-H bond angle.
c)
(6 marks)
The overall dipole moment of NH3 is 1.42 D. Calculate the dipole moment of an
individual N-H bond.
(6 marks)
d)
In two-dimensional space, the rotation matrix that transforms the coordinates
(x,y) to (x2,y2) is given by
(x2,y2)
R(0) = [cos-sine],
0
(x₁₁)
where
| = R()]
x
Fig. 1. Transformation
of (x,y) to (x2,y2) by
rotation about angle 0.
A sketch illustrating the angle 0 and the coordinates (x,y) and (x2,y2) is given in
Fig. 1. Show that the three H atoms in NH3 are spaced 120° apart. (7 marks)
3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F57b2fed4-3d32-4e81-b328-89f646bd1885%2F9eeecd2f-4813-463c-ac63-ae64ac592ebf%2Fjod9h5e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 2
The ammonia molecule, NH3, has a trigonal pyramidal molecular shape. Its Cartesian
coordinates are given below.
Atom
X/A
Y/A
Z/Å
N
0.000000
0.000000
0.096922
H
0.000000
0.969142
-0.226150
H
-0.839302
-0.484571
-0.226150
H
0.839302
-0.484571
-0.226150
a)
Calculate the length of the N-H bond.
(6 marks)
b)
Calculate the H-N-H bond angle.
c)
(6 marks)
The overall dipole moment of NH3 is 1.42 D. Calculate the dipole moment of an
individual N-H bond.
(6 marks)
d)
In two-dimensional space, the rotation matrix that transforms the coordinates
(x,y) to (x2,y2) is given by
(x2,y2)
R(0) = [cos-sine],
0
(x₁₁)
where
| = R()]
x
Fig. 1. Transformation
of (x,y) to (x2,y2) by
rotation about angle 0.
A sketch illustrating the angle 0 and the coordinates (x,y) and (x2,y2) is given in
Fig. 1. Show that the three H atoms in NH3 are spaced 120° apart. (7 marks)
3
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