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05:58How much energy would be required to break a helium nucleus into its constituents, two protons and two neutrons? The rest 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 nucleus.)
The Sun radiates energy at a rate of about 4 x 10²⁶ W.
(a) At what rate is the Sun’s mass decreasing?
(b) How long does it take for the Sun to lose a mass equal to that of Earth?
(c) Estimate how long the Sun could last if it radiated constantly at this rate.
A spaceship and its occupants have a total mass of 160,000 kg. The occupants would like to travel to a star that is 32 light-years away at a speed of 0.70c. To accelerate, the engine of the spaceship changes mass directly to energy.
(a) Estimate how much mass will be converted to energy to accelerate the spaceship to this speed.
(b) Assuming the acceleration is rapid, so the speed for the entire trip can be taken to be 0.70c, determine how long the trip will take according to the astronauts on board.
A quasar emits familiar hydrogen lines whose wavelengths are 8.5% longer than what we measure in the laboratory.
(a) Using the Doppler formula for light, estimate the speed of this quasar.
(b) What result would you obtain if you used the “classical” Doppler shift discussed in Chapter 16?
What minimum amount of electromagnetic energy is needed to produce an electron and a positron together? A positron is a particle with the same mass as an electron, but has the opposite charge. (Note that electric charge is conserved in this process. See Section 37–5.)
A pi meson of mass mπ decays at rest into a muon (mass mμ) and a neutrino of negligible or zero mass. Show that the kinetic energy of the muon is Kμ = (mπ - mμ)² c² / (2mπ).
