28.6 Relativistic energy  (Page 8/12)

Given the fact that light travels at $c$ , can it have mass? Explain.

If you use an Earth-based telescope to project a laser beam onto the Moon, you can move the spot across the Moon’s surface at a velocity greater than the speed of light. Does this violate modern relativity? (Note that light is being sent from the Earth to the Moon, not across the surface of the Moon.)

What is the rest energy of an electron, given its mass is $9\text{.}\text{11}\times {\text{10}}^{-\text{31}}\text{kg}$ ? Give your answer in joules and MeV.

Find the rest energy in joules and MeV of a proton, given its mass is $1\text{.}\text{67}\times {\text{10}}^{-\text{27}}\text{kg}$ .

If the rest energies of a proton and a neutron (the two constituents of nuclei) are 938.3 and 939.6 MeV respectively, what is the difference in their masses in kilograms?

The Big Bang that began the universe is estimated to have released ${10}^{\text{68}}\text{J}$ of energy. How many stars could half this energy create, assuming the average star’s mass is $4\text{.}\text{00}\times {\text{10}}^{\text{30}}\text{kg}$ ?

A supernova explosion of a $2\text{.}\text{00}\times {\text{10}}^{\text{31}}\text{kg}$ star produces $1\text{.}\text{00}\times {\text{10}}^{\text{44}}\text{kg}$ of energy. (a) How many kilograms of mass are converted to energy in the explosion? (b) What is the ratio $\mathrm{\Delta }m/m$ of mass destroyed to the original mass of the star?

(a) Using data from [link] , calculate the mass converted to energy by the fission of 1.00 kg of uranium. (b) What is the ratio of mass destroyed to the original mass, $\mathrm{\Delta }m/m$ ?

(a) Using data from [link] , calculate the amount of mass converted to energy by the fusion of 1.00 kg of hydrogen. (b) What is the ratio of mass destroyed to the original mass, $\mathrm{\Delta }m/m$ ? (c) How does this compare with $\mathrm{\Delta }m/m$ for the fission of 1.00 kg of uranium?

There is approximately ${10}^{\text{34}}\text{J}$ of energy available from fusion of hydrogen in the world’s oceans. (a) If ${10}^{\text{33}}\text{J}$ of this energy were utilized, what would be the decrease in mass of the oceans? Assume that 0.08% of the mass of a water molecule is converted to energy during the fusion of hydrogen. (b) How great a volume of water does this correspond to? (c) Comment on whether this is a significant fraction of the total mass of the oceans.

A muon has a rest mass energy of 105.7 MeV, and it decays into an electron and a massless particle. (a) If all the lost mass is converted into the electron’s kinetic energy, find $\gamma$ for the electron. (b) What is the electron’s velocity?

A $\pi$ -meson is a particle that decays into a muon and a massless particle. The $\pi$ -meson has a rest mass energy of 139.6 MeV, and the muon has a rest mass energy of 105.7 MeV. Suppose the $\pi$ -meson is at rest and all of the missing mass goes into the muon’s kinetic energy. How fast will the muon move?

(a) Calculate the relativistic kinetic energy of a 1000-kg car moving at 30.0 m/s if the speed of light were only 45.0 m/s. (b) Find the ratio of the relativistic kinetic energy to classical.

Alpha decay is nuclear decay in which a helium nucleus is emitted. If the helium nucleus has a mass of $6\text{.}\text{80}\times {\text{10}}^{-\text{27}}\text{kg}$ and is given 5.00 MeV of kinetic energy, what is its velocity?