Angular Momentum: Spin 1/2 Quantum Number Clarification

AI Thread Summary
The discussion clarifies the concept of spin in quantum mechanics, specifically addressing the spin-1/2 nature of particles like electrons and protons. It highlights that while the spin quantum number is indeed 1/2, the total spin angular momentum is not simply 1/2 hbar but rather has components that can be calculated. The z-component of the spin angular momentum is 1/2 hbar, which is what the book refers to. The conversation suggests that the terminology used in the book may be misleading or imprecise. Understanding these distinctions is crucial for grasping angular momentum in quantum systems.
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Homework Statement



Im reading about the electrom which apparently is spin -1/2

But doesn't this mean that s, i.e. the spin quantum number = 1/2. Surely the total spin it carries is root 3/2 hbar not 1/2 hbar? Yet in my book it says: "For example, in a hydrogen atom both the proton and the electron carry angular momentum 1/2hbar by virtue of their spins.."

Am I missing something?


Homework Equations





The Attempt at a Solution



Please see above..
 
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You are correct. 1/2 hbar would be the z-component of the spin angular momentum (the component along any axis), not the total angular momentum. I'd say the book was a bit sloppy.
 
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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