Gradient of a magnetic field dB = 0.2 T/m. A constant magnetic field is B0 = 4 T. Find the absolute and relative difference of the precession frequency of the hydrogen nuclei at the distance 20 cm along the gradient.

Find the binding energy per nucleon in J and eV for the three following isotopes, given their atomic masses in u: 33 Si silicon 32.97800017 u ☐ × 10-12 J ☐ MeV 241 Es einsteinium 241.0685424 u 99 ×10−12 J☐MeV 170 oxygen 16.9991317012 u ×10-¹² J MeV mhydrogen = 1.007825 u mneutron 1.008664915 u -27 u = 1.6605 × 101 kg

An unknown element X has the following isotopes: ⁶⁴X (49.00% abundant), ⁶⁶X (28.00% abundant), ⁶⁸X (23.00% abundant). What is the average atomic mass in amu of X?

A beam of alpha particles is incident on a target of lead. A particular alpha particle comes in “head-on” to a particular lead nucleu and stops 6.50 * 10-14 m away from the center of the nucleus. (This point is well outside the nucleus.) Assume that the lead nucleus, which has 82 protons, remains at rest. The mass of the alpha particle is 6.64 * 10-27 kg. (a) Calculate the electrostatic potential energy at the instant that the alpha particle stops. Express your result in joules and in MeV. (b) What initial kinetic energy (in joules and in MeV) did the alpha particle have? (c) What was the initial speed of the alpha particle?