Reference no: EM13488409

Recently, a new element has been isolated, temporarily named Ununseptium, with atomic number 117. The longest-lived isotope obtained so far is 294Uus with an atomic mass of 294:2105 0:0007u.

(a) How many electrons does a neutral atom of 294Uus contain?

(b) What is the mass ms of one 294Uus atom, in SI units? Include the error estimate in your answer, using 1 atomic mass unit 1u = (1:660538920:00000007)10 27 kg.

Suppose that one 294Uus atom is confined within a particle detector, a one-dimensional box of length L = 200 pm.

(c) What is the lowest possible kinetic energy of the atom in the box ? (3 significant figures is sufficient)

(d) If you measured the velocity of the atom while it is in the detector, what answer would you get?

(e) What velocity does the atom have in the absence of such a measurement?

(f) What is the total energy Es of the 294Uus atom?

294Uus is unstable, and decays rapidly into other atomic species. One possible decay route is via emission of an a-particle (a Helium nucleus, mass ma = 4:0001u) to form element 115 (Uup), with atomic mass mp = 290:1959u. Assume that the initial kinetic energy of the 294Uus atom can be neglected, so that the atom is approximately stationary in the lab frame.

(g) The total mass of the decay products is less than the mass of the original 294Uus atom. What accounts for this "missing mass" ?

(h) Conservation of total energy before and after the collision implies

where Ea is the energy of the a particle, and Ep is the energy of the Uup atom.

Similarly, conservation of total momentum before and after the collision implies Using these formulas, prove that the final energy of the a-particle is given by

Hint: Solve for Ep, and use the mass-energy relation 

(i) Hence calculate the energy and velocity of the a-particle.