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I can't find on any good source (such as a textbook) a precise specification about the cases when Hund's rules (especially Hund's third rule) for an electronic configuration of atom are valid (the rules help to select the lowest energy state of a configuration). As far as I understood: Hund’s...

Homework Statement In picture, first-order reflection from the reflection planes shown occurs when an x-ray beam of wavelength ##0.260 nm## makes an angle ##\theta=63.8°## with the top face of the crystal. What is the unit cell size ##a_0##? Homework Equations Bragg law $$d=\frac{ n...

Consider chain of two radioactive decays ##A \to B\to C##. The equation that regulates ##N_B## is $${\frac {\mathrm {d} N_{B}}{\mathrm {d} t}}=-\lambda _{B}N_{B}+\lambda _{A}N_{A}$$ I can't understand why the activity of ##B## is get as ##\lambda_B N_B##, for example at page 20 here...

Thank you for the answer! By "differing by a constant" in the left side are you referring to the fact that the rest mass ##mc^2## is constant?

The average loss of energy in a material per unit length of a particle (in particular an electron, which is stable) is described by the quantity ##dE/dx##. - for ionization it is given by the Bethe-Bloch formula $$-\left\langle {\frac {dE}{dx}}\right\rangle ={\frac {4\pi }{m_{e}c^{2}}}\cdot...

Consider a proton-neutron system. Phenomenlogical nucleon-nucleon potentials contain exchange forces terms (Majorana, Bartlett and Heisenberg terms), which are linked to the symmetry of the state w.r.t. (for example) the exchange of isospin (i.e. charge). On the other hand proton and neutron...

Consider the following reaction of strong interaction (in a scattering process) $$n+\pi^+\to \Lambda_0+K^+\tag{1}$$ Then the particle ##\Lambda_0## formed decays with weak interaction $$\Lambda_0\to \pi^+ +p\tag{2}$$ For each decay process I measure the four momenta of ##K^+##, ##\pi^+##...

Thanks for the answer. But there is actually a time axis and it is vertical (going from down to up). I'm aware that antiparticles move backwards in time (in the picture it moves downward a bit) but the fact is that it moves from left to right "in space". Is this wrong? So actually (besides...

The (residual) strong force between nucleons can be desribed as - The exchange of a meson (from a nucleon to the other), as in picture b) - The exchange of a quark and an antiquark: in picture a) one nucleon "gives" a quark and receive an antiquark and it's the opposite for the other I do...

The potential energy associated to the interaction between nucleons has its minimum (point of equilibrium) at ##r\sim 0.7 fm##, as showed in the following graph: Nevertheless, there are two facts that are, apparently, in contrast with this: - The average distance between nucleons is...

In particle phyisics four-momentum is used and De Broglie relation is used to understand what lenghts can be "seen" in an experiment. Here (page 6) https://people.phys.ethz.ch/~pheno/PPP/PPP2.pdf it is claimed Where ##Q^2## is not actually "momentum" but its the square of the four momentum...

The deuterium exists only with the proton and neutron of aligned spin, which suggests that the residual strong force is greated with aligned spins, i.e. the binding energy is greater if the spins are aligned. On the other hand the mass of ##\Delta^{+}## is greater than the mass of proton ##p##...

Consider the pairing term in Weizsäcker formula. Here https://en.wikipedia.org/wiki/Semi-empirical_mass_formula#Pairing_term it is claimed that: I don't understand how Pauli exclusion principle should be the cause of this. This term comes from spin-spin interaction (or "coupling"), but I do...

Consider a scattering between two particles a and b that produces two particles c and d: d is stable, while c decays in two other different particles e and f. The first interaction is by strong force (time of interaction ##t_1\sim 10^{-23}s##, which is also the time of generation of c and d)...

Homework Statement Consider the following reaction $$\mathrm{Ni^{2+}_{(aq)} + H_2S_{(g)} \to Ni_{(s)} + S_{(s)} + 2H^{+}_{(aq)}}$$ What are the activities of the terms in the reaction? Homework Equations The activity is defined as ##a = c/c^\circ## in ##\mathrm{ mol \, dm^3}## 3. The...

Consider the Kirkoff integral theorem and the Huygens -Fresnel principle/formula (both from Wikipedia): KIT The Kirchoff integral for monochromatic wave is: $$U({\mathbf {r}})={\frac {1}{4\pi }}\int _{S'}\left[U{\frac {\partial }{\partial {\hat {{\mathbf {n}}}}}}\left({\frac...

Maxwell stress tensor ##\bar{\bar{\mathbf{T}}}## in the static case can be used to determine the total force ##\mathbf{f}## acting on a system of charges contanined in the volume bounded by ##S## $$ \int_{S} \bar{\bar{\mathbf{T}}} \cdot \mathbf n \,\,d S=\mathbf{f}= \frac{d}{dt} \mathbf...

I don't uderstand how, using special relativity theory (time dilatation and length contraction), one can explain why in the Michelson interferometer there is no delay between the two rays in the reference frame where the interferometer is moving. Consider the picture ##2.## Setting...

EDIT OF THE QUESTION: I apologize, I made a mistake, I intended to write the first two maxwell equations, that are ##\nabla \cdot E=0## and ##\nabla \cdot B=0## (if there are no sources). ##E## and ##B## are intended to be vectors.

Consider a waveguide with axis parallel to axis ##z##. Using cartesian coordinates the fields inside the waveguide can be written as Where ##\alpha## is the wavenumber and ##k=\frac{\omega}{c}## . The maxwell equations ##\nabla \times E=-\frac{\partial B}{\partial t}## and ##\nabla \times...

In the experiment of the determination of ##h## using the photoelectric effect produced by light emitted by led's there is the systematic problem of the "dark current" or "back current", i.e. the current caused by photoelectric effect on the anode of the system which is used in the expreriment...

Suppose that I use a prism (vertex angle ##\alpha##) spectroscope to analyze a beam of visible light from a mercury lamp (different wavelenghts) and I want the determine the refraction index of the prism using the minmum deviation angles ##D_{min}##...

The focal of the lens equivalent of two thin lens at distance h is $$1/f=1/f_1+1/f_2+h/(f_1 f_2)$$ Therefore, supposing that ##f_1>0## and ##f_2>0## (both lenses are convergent), if ##f_1+f_2 <h## then the equivalent lens should be divergent. Nevertheless consider the example in picture...

Homework Statement Draw the ray diagram of the case of a diverging lens where both object and image are virtual, that is ##f<0## , ##p<0## with ##p<f## Homework Equations The Attempt at a Solution I did not find this particular case of ray diagram in any textbook so I would like to know...

Maxwell equation in absence of charges and currents are $$\nabla \cdot \bf{E} = 0 \\ \nabla\cdot B=0 \\ \nabla \times E=-\frac{\partial B}{\partial t} \\\nabla \times B=\mu \epsilon \frac{\partial E}{\partial t}$$ Wave equation is $$\nabla ^2 \bf{E}=\mu \epsilon \frac{\partial^2...

Homework Statement Consider a glass plate of refraction index n and thickness ## \Delta x ## placed between a point monochromatic source S and an observer O, as in picture. (a) Prove that, if absorption from the plate is neglegible, then the effect on the wave received by O is the add of a...

In Purcell- Electricty and Magnetism book, in the chapter on electromagnetic induction, I found the following explanation regarding the magnetic flux through a circuit of area ##S##. Consider the circuit in figure, moving in a time ##dt## in a magnetic field ##B##, constant in time (but not...

I have a doubt on this calculation of magnetic field in presence of displacement current. Consider a capacitor of radius ##R## and with plates at distance ##d## being charged: there is a displacement current in it. Suppose that I want to calculate the magnetic field ##B## at a distance ##r <...

Suppose that the Taylor series of a function ##f: (a,b) \subset \mathbb{R} \to \mathbb{R}## (with ##f \in C^{\infty}##), centered in a point ##x_0 \in (a,b)## converges to ##f(x)## ##\forall x \in (x_0-r, x_0+r)## with ##r >0##. That is $$f(x)=\sum_{n \geq 0} \frac{f^{(n)}(x_0)}{n!} (x-x_0)^n...

Homework Statement A cylindrical conductor of radius ##a## has a hole of radius ##b## and there is a current ##i## uniformly spread inside the conductor. Calculate the magnetic energy of the conductor. Homework Equations $$U_{m}=\int_{Volume} \frac{B^2}{2 \mu_0} dV$$ The Attempt at a...

A simple method to find the potential of a conservative vector field defined on a domain ##D## is to calculate the integral $$U(x,y,z)=\int_{\gamma} F \cdot ds$$ On a curve ##\gamma## that is made of segments parallel to the coordinate axes, that start from a chosen point ##(x_0,y_0,z_0)##. I...

Thanks for the reply! I see that there are some problems in that contact with the conservation of energy, but I'm a bit confused. Which work is lost when there is contact? The external forces or the electrostatic forces one? So what part of potential energy should I consider? After the contact...

Homework Statement Two metal spheres of equal radius ##R## are placed at big distance one from the other. Sphere 1 has total charge ##q## and sphere 2 has no charge. The two speheres are moved one towards the other until they touch, then they are moved again far away one from the other. What is...

I'm a Physics student currently ending the bachelor degree. Since I study in Europe (Italy) there are quite big differences in the degrees system between Europe, UK and USA. Start from the assumption that I would like in the future to do a PhD in the UK or in USA. My main question is: do a MSc...

I'm a Physics student ending the bachelor degree in Physics. I'm strongly interested in Condensed Matter Physics (both theoretical and experimental), especially the quantum mechanical aspects that are linked to this field of studies. I'm trying to choose where to study for a MSc in Physics...

I'm a bachelor student in Physics and I would like to continue with a MSc in the field of Condensed Matter Physics. I have to choose between some courses at my university and, since I'm not already an expert in Condensed Matter I would like to have a suggestion. If you were in my situation and...

What is the change in entropy of thermodynamic environment if it changes its temperature during the process and the process is not reversible? I'm slightly confused because, on the one side, in that case ##\Delta S_{gas} \neq -\Delta S_{surroundings}##, since ##\Delta S_{universe} >0## but on...

I do not understand why standing sound waves can be formed in a one-side or two-side open tube. Consider a one-side open tube. In particular how does the reflection of the wave at the open end occur? I found the following explanation. I do not get why the pressure at the open end cannot vary...

I think I miss something about energy of a mechanical wave. In absence of dissipation the mechanical energy transported by an harmonic wave is constant. $$E=\frac{1}{2} A^2 \omega^2 m$$ But, while studying normal modes on a rope, I find that the mechanical energy of a normal mode (still...

I'm confused about energy driven by a wave. Consider a sinousoidal wave moving in a rope. Each element ##dm## of the rope follows a simple harmonic motion in time. That means that the mechanical energy ##dE=dK+dU## of the element ##dm## is constant. Nevertheless on Halliday-Resnik-Krane I...

Hello, I’m doing my first year of bachelor degree in physics in Italy and I would really like to get some research experience before my third year. Do you know any (international) summer research opportunity for a physics student who completed his first or second year of studies? I would be ok...

Thanks a lot for the answers! I’m at the University, not at the Politecnico, since I didn’t like the Engeneering Physics program. I don’t understand what do you mean by “problem”, is it the reputation of the university or the tuition fees abroad? I know about the difficulty of getting the...

Hi, I'm an undergraduate physics student in Turin (Northern Italy), currently in the first year of my bachelor degree. Before enrolling here in Turin, I thought a lot about going to sudy abroad because I would like to get a job somewhere in Europe or even outside it. But then, for several...