How much energy would be required to break a helium nucleus into its constituents, two protons and two neutrons? The masses of a proton (including an electron), a neutron, and neutral helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference is called the total binding energy of the He nucleus.)

The muon is an unstable subatomic particle witha mean lifetime of 2.2 μs, and about 10,000 muons reach everysquare meter of the earth's surface a minute. A muon has a linear momentum G, and after some short time it decays into two other elementary particles with masses m1 and m2. The energy Q released during the decay is converted entirely into the kinetic energy of the decay products (i.e., into kinetic energy of m1 and m2). Find linear momenta of decay products. Draw a vector diagram showing a range of momenta decay products can take.

The carbon isotope 14C is used for carbon dating of objects.  A  14C nucleus can change into a different kind of element, a neighbor on the periodic table with lower mass, by emitting a beta particle – an electron or positron – plus a neutrino or an anti-neutrino.  Consider the scenario where 14C ( mass of 2.34 x 10 -26) decays by emitting an electron and anti neutrino.  The electron has a mass of 9.11x 10-31 kg and a speed of 5.5 x107  m/s.  While the anti neutrino has  a momentum of 8.5x10-24 kg-m/s.  If the electron and anti neutrino are emitted at right angles from each other, calculate the recoil speed of the nucleus.

dx 4x 3. In so-called "natural units" (which is just a sneaky way to let us ignore a bunch of constants), the relativistic kinetic energy of a rigid body is given by the formula 1 КЕ — т V1 – v2 where m is the rest mass of the body and v is its relative speed. Alien scientists on a space station are observing an object falling into a black hole. As the object falls, it is disintegrating, losing mass at a rate of 3 (so its mass is changing at a rate of -3). How fast is the kinetic energy of the main part of the object changing when its mass is 20, its velocity is .7, and it is accelerating at a rate of .1 (remember that acceleration is the derivative of velocity with respect to time: a = dt 1Note that this formula does not make sense when v > 1. That is because in natural units, a speed of 1 corresponds to the speed of light, and nothing with positive rest mass can go that fast.

Protons in a University accelerator are accelerated to a kinetic energy of 16 times their rest energy. (a) What is the relativistic factor gamma for these protons? (b) What is the speed of these protons? (express in terms of c, the speed of light) (c) What is their kinetic energy in MeV? (d) What is the rest energy of the protons? (e) What is their momentum in MeV/c?

A futuristic rocket ship of mass m,hip = 6.0 × 10° kg is sent into space carrying one person with the goal of traveling to nearby stars. The ship uses a newly discovered matter-antimatter drive that converts matter into energy at 100% efficiency. We will take Earth as the rest frame. For parts (a) through (d) you are interested in the portion of the spaceship's travel where it is using its drive to convert matter into the kinetic energy of the ship. (a) What is the speed of the ship when the work done by the ship's drive is equal to 150,000 TWh (the total energy used by humanity in 2014)? (b) How much work must the drive do for the rocket to reach a final speed of 0.95c? (c) How much matter would the drive need to annihilate in order for the ship to reach the final speed of 0.95c? Assume that the matter used in the antimatter drive is collected from the interstellar medium and that the mass of the ship remains constant. (d) When at the final speed of 0.95c, by what factor is the ship's…

Suppose that you have found a way to convert the rest energy of any type of matter directly to usable energy with an efficiency of 61.0%. How many liters of water would be sufficient fuel to very slowly push the Moon 1.70 mm away from the Earth? The density of water is ?water=1.00kg/liter, the Earth's mass is ?earth=5.97×1024 kg, the Moon's mass is ?moon=7.36×1022 kg, and the separation of the Earth and Moon is ?E,M=3.84×108 m.

In a collider two protons are accelerated until they have kinetic energies of 1000 MeV (as seen in the lab). The pair is then split and brought around circular paths so that they are directed at each other. What speed of approach would one proton see the other as having? The mass of a proton is 1.673x10-27 kg (or 1.007276 u), and the rest mass energy of a proton is 938.3 MeV. (Speed is a scalar, so your answer will not need a direction.) K= 1000 MeV K = 1000 MeV

Nuclear Fusion Reaction In a human-scale model of a nuclear fusion reaction, two "deuterons" smash together head-on. Each has a mass of 2.0147kg and is moving at speed vd. The result is a "Helium-3 nucleus" (mass 3.0160kg) and a separate "neutron" (mass 1.0090kg пс ). Amazingly, this reaction produces a positive Wn of 3.96 × 10 14 J -- by converting mass into kinetic energy as predicted by Einstein's E = mc². The "neutron" moves with a speed of un after the reaction. E 4 Vd 1.63×107 m S Type your answer... + D D 3Не N. Proton Neutron http://fusion.srubar.net Un ×107: m S &

The Sun produces energy at a rate of 4.00 x 1026 W by the fusion of hydrogen. How many kilograms of mass is the Sun losing per second?