A nucleus of helium with mass 5 amu breaks up from rest into a nucleus of ordinary helium (mass = 4 amu) plus a neutron (mass = 1 amu). The energy liberated in the break-up is 0.89 MeV, which is shared (not equally) by the products in the form of kinetic energy.
a) Using the conservation of momentum find the kinetic energy of the neutron.
b) The lifetime of the original nucleus is 1.0E-21 s. Because we are not sure when during this lifetime this reaction will occur (i.e., decay), the uncertainty of the time is equal to the lifetime. What range of values of the neutron kinetic energy might we measure in the laboratory as a result of the uncertainty relationship?
a) Since the He-5 nucleus is initially at rest, the initial momentum is 0. And since even in quantum mechanics, momentum is conserved, that means that the final momentum will also be zero:
1. p(He-5) = 0 = p(n0) + p(He-4),
where p(n0) is the momentum of the free neutron and p(He-4) is the momentum of the product nucleus of He-4. From here on in, I will just refer to the He-4 nucleus as "He."
Rearranging (1), we get
2. p(n0) = -p(He),
and from the definition of momentum, this means
3. m(n0)*v(n0) = -m(He)*v(He).
Plugging in masses in amu, and calling v(n0) = u, and v(He) = U,
4. u = -4U.
We also know the total kinetic energy of the products,
5. K(tot) = K(n0) + ...
How a nucleus of helium breaks up from rest into a nucleus of ordinary helium plus a neutron.
The rise of the Euro and the fall of the USD; Could the Euro replace the US Dollar?
The U.S. Dollar has been a very popular currency to hold worldwide as it has had a reputation for being stable and is accepted in exchange for goods and services in most corners of the globe. However, on January 1st, 1999 the European Union introduced the Euro, which has been accepted as the main currency in a growing number of European countries including Germany, France, Italy, Spain, Greece etc.. As a further challenge to the dominance of the USD China has started pressing to replace the USD as the world's reserve currency with the International Monetary Fund's (IMF) Special Drawing Rights as well as the World Bank's suggestion that the dollar should once again be linked to gold. Lately the Chinese have started proting their own currency too.
Is the exchange rate (the dollar price of the Euro) determined by a fixed or a floating exchange rate system? Is the exchange rate of the Mexican peso in terms of Euro determined in a fixed or in a floating exchange rate system? What about the IMF's Special Drawing Rights: How is their value determined? What about the large amount of money being printed by the Federal Reserve and the huge deficits being created by the US administration? What about the deficit/debt problems of the "Club Med" countries and the effect these problems are having on the value of the euro?
Will the Euro and/or the IMF's Special Drawing Rights or a gold linked dollar or a select basket of currencies replace the US Dollar as the world's most popular currency to hold? Consider the implications being introduced by the debt problems in Europe on the exchange rates between the U.S. dollar, the euro and the other major world currencies.
A paper detailing why the US dollar might be replaced as the world's reserve currency by the Euro or the IMF's Special Drawing Rights.View Full Posting Details