A steady beam of alpha particles (q = +2e), each traveling with kinetic energy of 24 MeV, carries a current of I = 260 nA. a) If the beam is directed perpendicular to a planar surface, how many alpha particles strike the surface in 3 s? b) Through what potential difference was it necessary to accelerate each alpha particle from rest to bring it to a kinetic energy of 24 MeV

Respuesta :

Answer with Explanation:

We are given that

q=+2 e

K.E=24 MeV=[tex]24\times 10^6e V[/tex]

[tex]1 MeV=10^6e V[/tex]

Current,I=260 nA=[tex]260\times 10^{-9} A[/tex]

a.Time,[tex]\Delta t[/tex]=3 s

We know that

Number of alpha particles,N=[tex]\frac{T\Delta t}{q}[/tex]

Using the formula

[tex]N=\frac{260\times 10^{-9}\times 3}{2\times 1.6\times 10^{-91}}[/tex]

Where [tex] e=1.6\times 10^{-19} C[/tex]

[tex]N=2.4375\times10^{12}[/tex]

b.Potential difference,V=[tex]\frac{K.E}{q}[/tex]

Using the formula

[tex]V=\frac{24\times 10^6 e}{2e}=12\times 10^6 V[/tex]