The electrons that are used in an electron microscope are accelerated through a potential difference of 70 kV.a. Calculate the speed of the electrons using the Newtonian formula for kinetic energy.b. Calculate the speed of the electrons using the relativistic formula for kinetic energy.c. By what factor does the Newtonian result exceed the relativistic result?

(a) Beta decay is nuclear decay in which an electron is emitted. If the electron is given 0.750 MeV of kinetic energy, what is its velocity? (b) Comment on how the high velocity is consistent with the kinetic energy as it compares to the rest mass energy of the electron.

A chain of nuclear reactions in the Suns core converts four protons into a helium nucleus. (a) What is the mass difference between four protons and a helium nucleus? (b) How much energy in MeV is released during the conversion of four protons into a helium nucleus?

Alpha decay is nuclear decay in which a helium nucleus is emitted. If the helium nucleus has a mass of 6.801027 kg and is given 5.00 MeV of kinetic energy, what is its velocity?

The sun energy at a rate of 3.85×10 26 W by the fusion of hydrogen. About 0.7% of each kilogram of hydrogen goes into the energy generated by the Sun. (a) How many kilograms of hydrogen undergo fusion each second? (b) If the sun is 90.0% hydrogen and half of this can undergo fusion before the sun changes character, how long could it produce energy at its current rate? (c) How many kilograms of mass is the sun losing per second? (d) What fraction of its mass will it have lost in the time found in part (b)?

The radius of circular electron orbits in the Bohr model of the hydrogen atom are given by (5.29 1011 m)n2, where n is the electron's energy level (Fig. P6.79). The speed of the electron in each energy level is (c/137n), where c = 3 108 m/s is the speed of light in vacuum, a. What is the centripetal acceleration of an electron in the ground state (n = 1) of the Bohr hydrogen atom? b. What are the magnitude and direction of the centripetal force acting on an electron in the ground state? c. What are the magnitude and direction of the centripetal force acting on an electron in the n = 2 excited state?

An astronaut wishes to visit the Andromeda galaxy, making a one-way trip that will take 30.0 years in the space-ships frame of reference. Assume the galaxy is 2.00 million light-years away and his speed is constant. (a) How fast must he travel relative to Earth? (b) What will be the kinetic energy of his spacecraft, which has mass of 1.00 106 kg? (c) What is the cost of this energy if it is purchased at a typical consumer price for electric energy, 13.0 cents per kWh? The following approximation will prove useful: 11+x1x2forx1

(a) What is the kinetic energy in MeV of a ray that is traveling at 0.998c? This gives some idea of how energetic a ray must be to travel at nearly the same speed as a ray. (b) What is the velocity of the ray relative to the ray?

What is the velocity of an electron that has a momentum of 3.041021kgm/s ? Note that you must calculate the velocity to at least four digits to see the difference from c.

An interstellar space probe is launched from Earth. After a brief period of acceleration, it moves with a constant velocity, 70.0% of the speed of light. Its nuclear-powered batteries supply the energy to keep its data transmitter active continuously. The batteries have a lifetime of 15.0 years as mean red in a rest frame. (a) How long do the batteries on the space probe last as measured by mission control on Earth? (b) How far is the probe from Earth when its batteries fail as measured by mission control? (c) How far is the probe from Earth as measured by its built-in trip odometer when its batteries fail? (d) For what total time after launch are data received from the probe by mission control? Note that radio waves travel at the speed of light and till the space between the probe and Earth at the time the battery fails.