Question

In some Rutherford scattering experiments, the alpha particles had kinetic energies of 9.3 MeV . What’s the speed of such an alpha particle?

Answer 1

Speed of an alpha particle is,
`v=2.11* 10^7\ m/s`

Step-by-step explanation:

It is given that,

Kinetic energy of the alpha particles,
`E=9.3\ MeV=9.3* 10^6\ eV`

Since,
`1\ eV=1.6* 10^(-19)\ J`

Kinetic energy,
`E=1.48* 10^(-12)\ J`

We need to find the speed of alpha particle. The kinetic energy os given by :

`E=(1)/(2)mv^2`

m is the mass of alpha particle,
`m=6.64* 10^(-27)\ kg`

`v=\sqrt{(2E)/(m)}`

`v=\sqrt{(2* 1.48* 10^(-12))/(6.64* 10^(-27))}`

v = 21113576.97 m/s

or

`v=2.11* 10^7\ m/s`

So, the speed of such an alpha particle is
`2.11* 10^7\ m/s`. Hence, this is the required solution.