Respuesta :
Answer:
The time taken for the alpha particle is 5.301x10⁻⁷s
Explanation:
The centripetal force is equal:
[tex]F=\frac{mv^{2} }{r}[/tex]
The magnetic force is equal:
[tex]F_{m} =Bqv[/tex]
Matching both expressions:
[tex]\frac{mv^{2} }{r} =Bqv\\r=\frac{mv}{Bq}[/tex]
Where
m = 6.64x10⁻²⁷kg
v = 4.8x10⁵m/s
B = 0.123 T
q = 1.6x10⁻¹⁹C
[tex]r=\frac{6.64x10^{-27}*4.8x10^{5} }{0.123*2*1.6x10^{-19} } =0.081m[/tex]
The time taken for the alpha particle is:
[tex]t=\frac{\pi r}{v} =\frac{\pi 0.081}{4.8x10^{5} } =5.301x10^{-7}s[/tex]
The time taken for the alpha particle is [tex]5.301*10^{-7}s[/tex]
Centripetal Force:
- The force that is necessary to keep an object moving in a curved path and that is directed inward toward the center of rotation.
- It is given by:
[tex]F_c=\frac{mv^2}{r}[/tex] .........(i)
where,
m= mass of the body
v= velocity
r= radius
The magnetic force will be:
[tex]F_m=Bqv[/tex]............(ii)
Thus, on computing two equations:
[tex]\frac{mv^2}{r} =Bqv\\\\r=\frac{mv}{Bq}[/tex].............(iii)
Given:
- m = 6.64x10⁻²⁷kg
- v = 4.8x10⁵m/s
- B = 0.123 T
- q = 1.6x10⁻¹⁹C
Substituting the values in equation (iii).
[tex]r=\frac{6.64*10^{27}*4.8*10^5}{0.123*2*1.6*10^{-19}} \\\\r=0.081m[/tex]
The time taken for the alpha particle is:
[tex]t=\frac{\pi*r}{v}\\\\ t=\frac{3.14*0.081}{4.8*10^5} \\\\t=5.301*10^{-7}s[/tex]
Thus, the time taken for the alpha particle is [tex]5.301*10^{-7}s[/tex].
Find more information about Centripetal force here:
brainly.in/question/7166399
