Recent content by phyguy321

so the .6 keV is our uncertainty energy? so \Deltat =hbar/2E

Homework Statement the nucleus of 227Th decays to 223Ra and \alpha. the daughter nucleus is left in a short lived excited state and decays down to the ground state with the emission of an 80 keV gamma ray. the natural line width of this gamma ray is .6 keV. what is the lifetime of the excited...

Homework Statement what is \sum i1/3 from i=1 to n Homework Equations The Attempt at a Solution is there an expansion for this?

So my physics professor is around 68 and his grading methods drive us all up the walls. He's very old school and it seems as though he will pick one person a class and give them the A. His grading methods change from test to test so we never know how to present the material. In one test he'll...

frankly I don't really care about capturing the reason of the problem. I just need to get through this class and not have a W on my transcript. Abstract math and modern algebra are terrible awful aspects of math that i just can't grasp. so as long as that is something i can put down and get...

Homework Statement List all the ideals of Q[x] containing the element f(x) = (x2 + x - 1)3(x-3)2 Homework Equations The Attempt at a Solution Why would an ideal contain this element? when all ideals in Q[x] are defined by being divisible by (x-2)

Z6 \rightarrow Z2 \phi(a mod 6) = a mod 2. since if a \equivb mod 6 then a\equivbmod 2 since 2|6

So if f(x) is in J and J = {a(x)g(x): a(x) in F[x]} then f(x) = a(x)g(x) therefore g(x)|f(x)?

p is prime. so show a mod p + b mod p = (a+b) mod p and (ab) mod p = (a mod p)*(b mod p) how do i do that?

what does it mean that J is generated by g(x)? in layman's terms

so i have to find every set in Z that satisfies those equations by ending in Z? same goes for Z_2 to Z_6 find every set that will add together in the homomorphism in Z_2 and will separately add together in Z_6? is this what its asking? if so how do i show that?

Homework Statement Find all ring homomorphisms \phi: Z \rightarrow Z \phi: Z2 \rightarrow Z6 \phi: Z6 \rightarrow Z2 Homework Equations A function \phi: R \rightarrow S is called a ring homomorphism if for all a,b\inR, \phi(a+b) = \phi(a) + \phi(b) \phi(ab) = \phi(a)\phi(b) \phi(1R)...

Homework Statement Prove that \phi : Zp \rightarrow Zp, \phi (a) = a p is a ring homomorphism, find the ker \phi Homework Equations The Attempt at a Solution So show that a _{p} + b _{p} = (a + b)p? and (ab)p = (ap)(bp)?

Homework Statement Let I = <f(x)>, J =<g(x)> be ideals in F[x]. prove that I\subsetJ \leftrightarrow g(x)|f(x) Homework Equations The Attempt at a Solution If I is a subset of J then does that mean that f is in J also and by definition of an ideal g*some b in J must equal something...

Ok that makes sense, now what if we wanted the kinetic energies to differ by 1%? so 1/2mv^2 and \gammamc^2 - mc^2 differ by one percent? do i plug in the velocity from part a into the gamma and solve for v in the classical equation?