Homework Statement
[a) Show that chemical potential in intrinsic semiconductor at T = 0 lies exactly in the middle of the energy gap. At what temperature is the chemical potential equal ##(3/4)(E_c + E_v)##, where ##E_c## and ##E_v## are energies od the bottom of the conduction band and of the...
Homework Statement
Powder sample of monoatomic cubic lattice crystal is analyzed using Debye-Scherrer method. Primitive vetors of direct lattice are: a1 = (a, 0, 0), a2 = (0, a, 0) i a3 = (0, 0, a). Wavelength of x-ray radiation is 1 Å.
a) Find primitive vectors of reciprocal lattice.
b) Find...
Homework Statement
Using free electron model find the number of electron quantum states per unit volume in ##[\varepsilon_F, \varepsilon_F + \Delta \varepsilon]## energy interval of sodium. Fermi energy of sodium is ##\varepsilon_F = 3.22 eV##, and energy band width is ##\Delta...
I have one more question. Does it matter what charge I put at ##x_1##? I just inserted ##Q_3## in the ##F_{13}+F_{23}=0## equation and it doesn't matter if ##Q_3## is positive or negative. I always get ##0=0##. That would mean ##Q_3## can be positive or negative. Or not?
I get it, but I switched the plus sign to minus in ##k \cdot \frac{Q_1 \cdot (-Q_3)}{x_1^2}=-k \cdot \frac{Q_1 \cdot (-Q_3)}{x_1^2}##
Now I can divide equation by minus and I will get the same equation as was for positive ##Q_3##. Right?
I see I've made some typing errors and my notation for distance of ##Q_3## from charge ##Q_1## isn't appropriate. Also, when ##x_1=-3cm## charge ##Q_3## must be negative because it is closer to the positive charge. If it was positive, it'd be repelled. Thank you all for your help and pointing...
Homework Statement
Two point charges ##Q_1 = 9 \mu##C and ##Q_2 = -16 \mu##C are fixed in space on a distance r=7cm. At what distane ##x_1## from the first charge, and ##x_2## from the second charge, should we place the third charge ##Q_3## so that net force on ##Q_3## is zero? make a sketch...
Well, I could substitute ##\Theta_2##:
##mg=q \cdot E \cdot \tan(\Theta_2)##
##\tan(\Theta_{2})=\frac{mg}{q \cdot E}##
##\Theta_2=\arctan \frac{mg}{q \cdot E}##
What do I do now? Do I just say that ##\Theta_2## is 60% of 45 degrees which is 27 degrees?
Homework Statement
Charged metal sphere hanging on an isolated thread of negligible mass is put in a homogeneous horizontal electric field so that the thread makes a 45 degree angle with the el. field. What angle does the thread with the sphere close with the el. field after we remove 40% of...
I see. I could have stated that: ##pV^2=const##
and then from the pressure equation: ## const=\frac{1}{a}ln(\frac{S}{\gamma})##
Then I substitute variables in constant in order to get a dependence on T:
##pV^2=\frac{1}{a}ln(\frac{S}{\gamma}) \rightarrow apV^2=ln(\frac{S}{\gamma}) \rightarrow...
Regarding a mistake with (a) ##T=\frac{1}{aV} \cdot \frac{\gamma}{S} \cdot \frac{1}{\gamma}=\frac{1}{aSV}##
Thank you for noticing.
This leads to: ##C_V=(\frac{d}{dT})_V TSpaV^2=SpaV^2##
(b) The right formula: ##C_V=(\frac{dH}{dT})_p##
##H=U+pV=U+U=2U##
##C_p=(\frac{d}{dT})_p (2U)=2 \cdot...
Homework Statement
Find: (a) Equation of state $$f (p, V, T)$$ and (b) Adiabatic equation in dependence on volume and pressure. Internal energy $$U(V, S)=\frac{1}{aV} ln(\frac{S}{\gamma})$$ where a and ##\gamma## are positive constants.
Homework Equations
(a) ##dU=TdS-pdV \rightarrow##...