Analyzing False Statements about Orbitals

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The discussion focuses on identifying false statements regarding atomic orbitals. The user is uncertain about the validity of several claims, specifically regarding the orientations of p and d orbitals, and the energy levels of 3d and 4s orbitals in hydrogen and helium atoms. The user initially suspects statements b, c, and d to be false but later narrows it down to b and c. Clarification and verification of these statements are requested from other participants. Accurate understanding of orbital characteristics is essential for grasping quantum chemistry concepts.
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I was able to work through most of them myself but am haveing problems with the following, for some I simply don't understand the statement it self. Any help appericiated.
Pick the false statements out of the following:


a. Different p orbitals with the same value of the principal quantum number have different orientations in space.
b. Only three different orientations are possible for 3d orbitals.
c. A dxy orbital has maximum electron density along the x and y axes directions.
d. For the hydrogen atom, a 3d orbital is of higher energy than a 4s orbital.
e. For helium atom, a 3d electron is of higher energy than a 3s electron.

I think b, c, and d are false, but am very unsure.
 
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I just read-up on the topic a bit more, I now think that only b and c are false. Can someone pleasr verify?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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