Why is there uneven spacing in the P and R branches of a vibration rotation spectra?

An ideal gas that goes through a cyclical process on a PV diagram and returns to the location on the PV diagram where it began. analyze changes in temperature and thermal energy of the gas change during the cycle. Analyze transfers of energy through heat and work during various stages of the cycle.

note: including formulas in the analysis would be helpful.

Two protons are brought from very far apart to a distance of 1×10−15 m and kept there. Then, an electron is brought to point A, equidistant from both protons and forming an equilateral triangle with the two protons. The electron is let go and passes through point B, the midpoint between protons. Determine: a. The electrostatic force between proton? b. The electric field at points A and B due to the protons

a one-dimensional box of length 2.7 nm

(1) Calculate the wavelength of electromagnetic radiation emitted when the photon makes a transition from n = 2 to n = 1. Answer in units of µm.

(2) Calculate the wavelength of electromagnetic radiation emitted when the photon makes a transition from n = 3 to n = 2. Answer in units of µm

(3) Calculate the wavelength of electromagnetic radiation emitted when the photon makes a transition from n = 3 to n = 1. Answer in units of µm.

A 700-kg elevator starts from rest. It moves upward for 4.50 s with constant acceleration until it reaches its cruising speed of 1.75 m/s. (a) What is the average power of the elevator motor during this time interval?

There are two identical, positively charged conducting spheres fixed in space. The spheres are 38.2 cm38.2 cm apart (center to center) and repel each other with an electrostatic force of ?1=0.0705 NF1=0.0705 N . A thin conducting wire connects the spheres, redistributing the charge on each sphere. When the wire is removed, the spheres still repel, but with a force of ?2=0.100 NF2=0.100 N . The Coulomb force constant is ?=1/(4??0)=8.99×109 N⋅m2/C2k=1/(4πϵ0)=8.99×109 N⋅m2/C2 .

James has just jumped out of an airplane. After he opens his parachute he experiences 2 forces: the constant force of gravity, and a wind drag that is proportional to his velocity. His height may therefore follow the equation: d²h/dt² = -9.8 - 2(dh/dt). As a second-order differential equation, this is not technically solvable by separation of variables. However, because the variable h appears only in its derivatives, we can turn this into a first-order equation, and solve that by separation.

a) Letting v = dh/dt, rewrite the above equation as a first-order differential equation in v.

b) Your equation in part a suggests that there is one velocity for which dv/dt = 0. What is this velocity?

c) Solve your equation using separation of variables. Your solution should contain an arbitrary constant: call it C₁.

d) Calculate lim t to infinite v(t) and use it to describe what is physically happening to James after he's been in the air for a long time.

e) Now that you have a velocity function v(t), integrate it with respect to t to find a position function h(t). This will introduce a second constant C₂.

f) Suppose James begins at a height of 3000m with no initial velocity, what is his height 3s later?

A dielectric-filled capacitor consists of two parallel plates, each with an area  A = 15.0 cm2 , seperated by a distance of d = 10.0 mm and dielectric constant k = 4.00. A potential difference  V= 10.0 V  is applied to these plates . Throughout the problem, use ϵ0 = 8.85×10⁻¹² C2/N⋅m2

Part A)

Calculate the energy U1of the dielectric-filled capacitor.(J)

Part B)

The capacitor remains connected to the battery. Calculate the energy U2 of the capacitor at the moment when the capacitor is half-filled with the dielectric, because the dielectric is slowly pulled away. of(J)

Part C

The capacitor is now disconnected from the battery, and the dielectric plate is slowly removed the rest of the way out of the capacitor. Find the new energy of the capacitor, U3 of (J)

Part D)

In the process of removing the remaining portion of the dielectric from the disconnected capacitor, how much work W is done by the external agent acting on the dielectric? of (J)

t² (d²r/dt²) - 9t (dr/dt) + 16r = 4 is an example of a "Cauchy-Euler equation." Such equations appear in a number of physics and engineering applications.

a) Write the complementary homogeneous equation.

b) Plug r = e^kt into the equation you wrote in part a. Show that this solution will not work for any constant k: this equation has no exponential solution.

c) Plug the guess r = tⁿ (where n is a constant) into the equation you wrote for part a. Solve the resulting algebraic equation for n; you should find 2 solutions.

d) Write the general solution to the equation you wrote in Part a.

e) Find a specific solution to the origianl (inhomogeneous) equation.

f) Write the general solution to the inhomogeneous equation.

g) What is it about this particular equation that made r = tⁿ work?

make technology papers related to scattering

Over and over I'm getting into the same trouble, so I'd like to ask for some help.

1. I need to solve some basic electrodynamics problem, involving magnetic fields, moving charges or currents.
2. But I forgot all this rules about "where the magnetic field should go if the current flows up". I vaguely remember that it about hands or fingers or books or guns, and magnetic field should go somewhere along something, while current should flow along something else... But it doesn't help, because I don't remember the details.
3. I do find some very nice rule and use it. And I think "that one I will never forget".
4. ...time passes...
5. Go to step 1.

The problem is that you have to remember one choice from a dichotomy: "this way or that way". And all the mnemonics I know have the same problem -- I got to remember "left hand or right hand", "this finger or that finger", "inside the book or outside of the book".

Maybe someone knows some mnemonics, that do not have such problem?

make technology papers related to potential variations

Which is larger, an increment of 1°C, or of 1°F? Explain, using an example if needed.

An automobile tire is inflated with air originally at 10.0°C and normal atmospheric pressure. During the process, the air is compressed to 24.0% of its original volume and the temperature is increased to 48.0°C.

(a) What is the tire pressure in pascals?
Pa

(b) After the car is driven at high speed, the tire's air temperature rises to 85.0°C and the tire's interior volume increases by 3.00%. What is the new tire pressure (absolute) in pascals?
Pa

A mass m = 16 kg is pulled along a horizontal floor with NO friction for a distance d =8.4 m. Then the mass is pulled up an incline that makes an angle ? = 25