(a)
The moment of inertia of the hydrogen molecule about an axis through its center of mass and perpendicular to H-H bond.
(a)
Answer to Problem 13P
The moment of inertia of the hydrogen molecule about an axis through its center of mass and perpendicular to H-H bond is
Explanation of Solution
A hydrogen molecule makes a transition from ground level to
Write the formula for energy levels.
Here,
Refer equation (I) and find energy of
Here,
Refer equation (I) and find energy of
Here,
Refer equation (I) and find energy of
Here,
Write the formula for the energy difference between
Here,
Write the formula for the energy difference between
Here,
Subtract equation (III) from (II).
Re-write the above equation.
Re-write the above equation to obtain
Conclusion:
Substitute
The moment of inertia of the hydrogen molecule about an axis through its center of mass and perpendicular to H-H bond is
(b)
The vibrational frequency of the hydrogen molecule.
(b)
Answer to Problem 13P
The vibrational frequency of the hydrogen molecule is
Explanation of Solution
Refer section (a) and write the formula for the energy difference between
Here,
Re-write the above equation to get an expression for
Write the formula for
Here,
Conclusion:
Substitute
Substitute
The vibrational frequency of the hydrogen molecule is
(c)
The equilibrium separation distance for the molecule.
(c)
Answer to Problem 13P
The equilibrium separation distance for the molecule is
Explanation of Solution
Write the formula for the moment of inertia of the molecule.
Here,
Reduced mass of hydrogen molecule is half of the mass of it.
Here,
Re-write the above equation to get an expression for
Conclusion:
Substitute
The equilibrium separation distance for the molecule is
Want to see more full solutions like this?
Chapter 42 Solutions
Physics for Scientists and Engineers with Modern Physics
- In a Maxwell's wheel experiment, the mass of the wheel is 450 gram, and the radius of the spindle going through the center of the wheel is 3 mm. A student lets the wheel fall 30 cm, and finds out that the speed of the center of mass is 0.15 m/s. What is the moment of inertia of this wheel? Take g=9.81 m/s^2.arrow_forwardConsider an oxygen molecule (O2) rotating in the xy plane about the z axis. The axispasses through the center of the molecule, perpendicular to its length. The mass of each oxygen atom is 2.66 x 10-26 kg, and at room temperature the average separation between the two atoms is d=1.21 x 10-10 m (the atoms are treated as point masses). a) Calculate the moment of inertia of the molecule about the z axis. b) If the angular speed of the molecule about the z axis 4.60 x 1012 rad/s, what is its rotational kinetic energy?arrow_forwardA rod of mass M = 124 g and length L = 39 cm can rotate about a hinge at its left end and is initially at rest. A putty ball of mass m = 16 g, moving with speed V = 10 m/s, strikes the rod at angle θ = 29° a distance D = L/2 from the end and sticks to the rod after the collision. Calculate the rotational kinetic energy, in joules, of the system after the collision. I cannot figure this out. Can you please write each step? Thank youarrow_forward
- A rod of mass M=101g and length L=31cm can rotate about a hinge at its left end and is initially at rest. A putty ball of mass m=11g, moving with speed V=6m/s, strikes the rod at angle theta=21 degrees a distance D=L/3 from the end and sticks to the rod after the collision. Calculate the rotational kinetic energy, in joules, of the system after the collisionarrow_forwardA Solid sphere of mass 6 kg and radius 1.2 meters is rolling without slipping on a horizontal surface with a velocity of 2 m/s. It collides perfectly elastically with a Solid cylinder of mass 10 kg and radius .8 meters initially at rest. Find vf of the Solid sphere after the collision.arrow_forwardFrom classical physics, we know that angular momentum, moment of inertia, and angular velocity are related via L=100 and E= If the rotational energy is 941.5 J and the angular velocity is 9.2 sec-1, what is the moment of inertia (in kg-m²)? Report your answer as a decimal number to three significant figures.arrow_forward
- let's consider the three atoms composing the molecule have different masses and coordinate, while the axis of rotation is still y-axis. The first atom has a mass of 8.61 kg, with x coordinate at 3.063 m and y coordinate at 3.826 m. The second atom has a mass of 63.048 kg, with x coordinate at 87.738 m and y coordinate at 51.326 m. The third atom has a mass of 26.317 kg, with x coordinate at 42.334 m and y coordinate at 23.115 m. What is the moment of inertia in the unit of kg m2 with respect to the y axis?arrow_forwardLet's consider the three atoms composing the molecule now have different masses and coordinate, while the axis of rotation is still z axis that is perpendicular to the xy plane. The first atom has a mass of 142.54 kg, with x coordinate at 3 m and y coordinate at 6 m. The second atom has a mass of 82.55 kg, with x coordinate at 1 m and y coordinate at 6 m. The third atom has a mass of 8 kg, with x coordinate at 5 m and y coordinate at 9 m. What is the moment of inertia in unit of kg m2 with respect to the x axis?arrow_forwardOn a frictionless table, a 0.56 kg glob of clay strikes a uniform 1.26 kg bar perpendicularly at a point 0.35 m from the center of the bar and sticks to it. If the bar is 1.06 m long and the clay is moving at 9.30 m/s before striking the bar, what is the final speed of the center of mass?arrow_forward
- What are the components of the moment of inertia of the BeBr2 body if the coordinates of the heritage sites and masses are in the following table atom X (A) y(A) z(A) mass 0 Be 0 0 9u Br 1.9 0 0 80u 0 -1.9 080u a-lc-la-la b-lolla c- lc> lo= la d-Is=la> la a Please answer within O b 60 minutes O C O d oc حيث ان u=1.67x1027 Kgarrow_forwardThe uniform beam has a mass of 44 kg per meter of length. Determine the reactions at the supports. AD Answers: A, i i B₂ By= i 2.8 m- z z z 1.2 m 350 kg Barrow_forwardConsider an oxygen molecule (O2) rotating in the xy plane about the z-axis. The axis passes through the center of the molecule, perpendicular to its length. The mass of each oxygen atom is 2.66 x 10-26 kg, and at room temperature, the average separation between the two atoms is d=1.21 x 10-10 m (the atoms are treated as point masses). a) Calculate the moment of inertia of the molecule about the z-axis. b) If the angular speed of the molecule about the z-axis 4.60 x 1012 rad/s, what is its rotational kinetic energy?Answer: a) 1.95 x 10-46 kg.m2 b) 2.06 x 10-21 Jarrow_forward
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning