A diatomic hydrogen gas H₂ is composed of two atoms of hydrogen connected by a spring of spring stiffness k. The probability to find the atoms at a position x is given by: f(x) = {Aexp[-Bx] for 0≤x≤ ∞ elsewhere where A is the normalization constant and ẞ a constant characteristic of the gas. 1. Draw a graph of the probability function. 2. Find an expression of A in terms of B. 3. Using the average elastic potential of the spring connecting the two atoms find an expression of in terms of k. 4. Assuming that the centre of mass of the two atoms moves with a constant speed v = and using the total average translational kinetic energy of the centre of mass find an expression of k in terms of the mass of the hydrogen atom m and the time t. [Note that the centre of mass, M = m/2.] 5. Assuming that the atoms rotated around an axis which is the perpendicular bisector of the line joining the two atoms and using the average rotational energy of the atoms, taking 11 - ro ris the anaration distance between the atoms and on the angular sneed
A diatomic hydrogen gas H₂ is composed of two atoms of hydrogen connected by a spring of spring stiffness k. The probability to find the atoms at a position x is given by: f(x) = {Aexp[-Bx] for 0≤x≤ ∞ elsewhere where A is the normalization constant and ẞ a constant characteristic of the gas. 1. Draw a graph of the probability function. 2. Find an expression of A in terms of B. 3. Using the average elastic potential of the spring connecting the two atoms find an expression of in terms of k. 4. Assuming that the centre of mass of the two atoms moves with a constant speed v = and using the total average translational kinetic energy of the centre of mass find an expression of k in terms of the mass of the hydrogen atom m and the time t. [Note that the centre of mass, M = m/2.] 5. Assuming that the atoms rotated around an axis which is the perpendicular bisector of the line joining the two atoms and using the average rotational energy of the atoms, taking 11 - ro ris the anaration distance between the atoms and on the angular sneed
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![A diatomic hydrogen gas H₂ is composed of two atoms of hydrogen connected by a spring of
spring stiffness k. The probability to find the atoms at a position x is given by:
f(x) = {Aexp[-Bx] for 0≤x≤ ∞
elsewhere
where A is the normalization constant and ẞ a constant characteristic of the gas.
1. Draw a graph of the probability function.
2. Find an expression of A in terms of B.
3. Using the average elastic potential of the spring connecting the two atoms find an
expression of in terms of k.
4. Assuming that the centre of mass of the two atoms moves with a constant speed v =
and using the total average translational kinetic energy of the centre of mass find an
expression of k in terms of the mass of the hydrogen atom m and the time t. [Note that
the centre of mass, M = m/2.]
5. Assuming that the atoms rotated around an axis which is the perpendicular bisector of
the line joining the two atoms and using the average rotational energy of the atoms,
taking v = rw, r is the separation distance between the atoms and the angular speed,
show that the moment of inertia of the atoms is given by i
= 2mr².](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d23c93b-870e-4ad1-8eae-60e3d2381ea8%2F4e87d126-975c-4a01-91bc-6eff6f668b48%2F2okzo2_processed.png&w=3840&q=75)
Transcribed Image Text:A diatomic hydrogen gas H₂ is composed of two atoms of hydrogen connected by a spring of
spring stiffness k. The probability to find the atoms at a position x is given by:
f(x) = {Aexp[-Bx] for 0≤x≤ ∞
elsewhere
where A is the normalization constant and ẞ a constant characteristic of the gas.
1. Draw a graph of the probability function.
2. Find an expression of A in terms of B.
3. Using the average elastic potential of the spring connecting the two atoms find an
expression of in terms of k.
4. Assuming that the centre of mass of the two atoms moves with a constant speed v =
and using the total average translational kinetic energy of the centre of mass find an
expression of k in terms of the mass of the hydrogen atom m and the time t. [Note that
the centre of mass, M = m/2.]
5. Assuming that the atoms rotated around an axis which is the perpendicular bisector of
the line joining the two atoms and using the average rotational energy of the atoms,
taking v = rw, r is the separation distance between the atoms and the angular speed,
show that the moment of inertia of the atoms is given by i
= 2mr².
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