Question on KE of radioactive source

[faisal]

an alpha particle from a certain radioactive source has a Kinetic energy of 8.2x10(-13)j. Using the information below, estimate how long it would ctake this particle to travel a distance equal to the diameter of the atom.
mass of alpha particle= 6.6x10-27kg
diameter of atom=1x10-10m
my answer
KE=1/2MV2
V2=(KEX2)/M
(9.2X10-13X2)/6.6X10-27= THE Square root of 2.48
which is obviously wrong, can u guyz help me address the problem?

 

[Astronuc]

Determine the velocity, $$v = \sqrt{\frac{2\,KE}{m}}$$

and then t = v / d.

You may have a numercial error in (9.2X10-13X2)/6.6X10-27

KE = 8.2x10^-13 J = ~ 5.1 MeV, so it is non-relativistic.

m = 6.6x10^-27 kg

 

[faisal]

I don't get it?

 

[HallsofIvy]

an alpha particle from a certain radioactive source has a Kinetic energy of 8.2x10(-13)j. Using the information below, estimate how long it would ctake this particle to travel a distance equal to the diameter of the atom.
mass of alpha particle= 6.6x10-27kg
diameter of atom=1x10-10m
my answer
KE=1/2MV2
V2=(KEX2)/M
(9.2X10-13X2)/6.6X10-27= THE Square root of 2.48
which is obviously wrong, can u guyz help me address the problem?

Several points: first,you have "9.2" when I think you mean "8.2". I think that's just a typo since the "2.48" is correct.

Second, however, (9.2X10^-13x2)/6.6X10^-27 is not any where near "2.48"! Did you forget or simply not write the 10^-13/(6.6X10^-27? I get 2.48X10¹⁴.
The square root of that is 15763402 m/s.

Finally, according to your formula, that is the speed of the alpha particle. You were asked to find the time it would take to cross the diameter of an atom.