How Do You Calculate the Half-Life of a Radioactive Substance?

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Homework Statement


k so An experiment is done to determine the half-life of a radioactive substance that emits one beta particle for each decay process. Measurements show that an average of 8.4 beta particles are emitted each second by 2.5 milligrams of the substance. The atomic weight of the substance is 230. find the half-life of the substance...

Homework Equations


New Mass=Origonal mass(1/2) time/halflife

The Attempt at a Solution



i can't sort out where the 2.5 milligrams go, and how to measure the atomic weight properly, meaning, where i place it in the equation
 
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Number of radioactive atoms in 230 g is equal to the Avogadro's number. Find the number of atoms in 2.5 milligrams. Activity is given. It is proportional to the number of atoms. From this find lmbda. Using the relation between lambda and half life find the half life.
 
Thread 'Need help understanding this figure on energy levels'

Thread 'Need help understanding this figure on energy levels'

This figure is from "Introduction to Quantum Mechanics" by Griffiths (3rd edition). It is available to download. It is from page 142. I am hoping the usual people on this site will give me a hand understanding what is going on in the figure. After the equation (4.50) it says "It is customary to introduce the principal quantum number, ##n##, which simply orders the allowed energies, starting with 1 for the ground state. (see the figure)" I still don't understand the figure :( Here is...
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Thread 'Understanding how to "tack on" the time wiggle factor'

Thread 'Understanding how to "tack on" the time wiggle factor'

The last problem I posted on QM made it into advanced homework help, that is why I am putting it here. I am sorry for any hassle imposed on the moderators by myself. Part (a) is quite easy. We get $$\sigma_1 = 2\lambda, \mathbf{v}_1 = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \sigma_2 = \lambda, \mathbf{v}_2 = \begin{pmatrix} 1/\sqrt{2} \\ 1/\sqrt{2} \\ 0 \end{pmatrix} \sigma_3 = -\lambda, \mathbf{v}_3 = \begin{pmatrix} 1/\sqrt{2} \\ -1/\sqrt{2} \\ 0 \end{pmatrix} $$ There are two ways...
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