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Alpha decay is nuclear decay in which a helium nucleus is emitted. If the helium nucleus has a mass of$6.80 \times 10^{-27} \mathrm{kg}$ and is given 5.00 $\mathrm{MeV}$ of kinetic energy, what is its velocity?

$v=1.53 \times 10^{7} \mathrm{ms}^{-1}$

Physics 103

Chapter 28

Special Relativity

Relativity

Rutgers, The State University of New Jersey

University of Washington

Simon Fraser University

University of Winnipeg

Lectures

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An alpha particle ($m = 6.…

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Find the kinetic energy of…

they're 11. Still kind of think energies, given by relativistic connoting energy is equal to gamma minus one times M C. Square. Well, Emmy's moss off the material and C is the speed of light demise. The relativistic constant and it's equal to one divided by square root off one minus least were divided by C Square. Well, the most of the hill, you mean clears M is equal to six point ends. It'll multiply by, uh, 10 to the dollar, minus 27 kilogram. This is muscle pavilion nucleus and kinetic energy of the helium nucleus. Uh, can I get a receipt? Kinetic energy? Oh, relax. Mystic Connecticut or to your filial nucleus is equal to 5.0 1,000,000 electron walls and this can be written. It is 5.0 multiplied by since Maggie is 10 to the power six electron wolves. And further we have, uh, 5.0 multiplied by 10 to the power six and one electron. Walt is 1.6, multiplied by 10 $30 minus 19 Jules and multiplying the numbers, we get good 0.0 multiplied by 10 to the power minus 13. Jules and the speed of light. C equals 3.0 Multiply by 10 to the hour. Eight meter per second. And for there, uh, we can express. We is, uh, see into square Rudolph one minus, uh, one divided by want lis. Uh, kinetic energy. Relativistic divided by, uh, m square M c square on. But, uh, we have a spare here as well. Now, let's, uh, plug in the values C is three bond 00 Multiply by 10 to the power age into square. Rudolph Ah, square root off. One minus one. Divided by one less. Well, your leg, Mr. Gonna take energies. 8.0 multiplied by 10 to the power minus 13. Jules, divided by moss and moss, is 6.80 multiplied by 10 to the power minus 27 kilograms multiplied by C square, which is 3.0 multiplied by 10 to the power eight whole square. All right, and, uh, simply find this. We get Ah, we is equal to 3.0 amount of life. I tend to devour eight. Made a poor second, multiply by 0.0 point 05 Fun one. And this gives us Ah, we equals 1.53 Multiply by. Tend to the power. Seven meter per second

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