Respuesta :
[tex]\frac{mv}{qB}[/tex]Answer:
a) ratio of radii for same momentum = 1
b) ratio of radii for same energy = 2.3 × [tex]10^{-2}[/tex]
Explanation:
using formula for radius
r = [tex]\frac{mv}{qB}[/tex]
where m is mass
v is velocity
q is charge
B is magnetic field
a) for same momentum radius will be inversely proportional to roduct of charge and magnetic and magnetic field
r ∝ [tex]\frac{1}{qB}[/tex]
since for proton and electron s charge and magnetic field is same so
[tex]\frac{r_{1} }{r_{2} } =\frac{1}{1}[/tex]
b) using relation b/w kinetic energy and momentum
p = [tex]\sqrt{2 KEm}[/tex] ............(1)
where p is momentum and
K.E is kinetic energy
we know [tex]r =\frac{mv}{qB}[/tex]
[tex]mv =qBr[/tex]
[tex]p = mv[/tex] = [tex]qBr[/tex]
from first equation
[tex]qBr = \sqrt{2KEm}[/tex]
since qB is same for electron and proton and energy is also same(given)
so we get
[tex]\frac{r_{e} }{ r_{p} }[/tex][tex]= \sqrt{\frac{m_{e} }{m_{p } }[/tex]
[tex]\frac{r_{e} }{r_{p} }[/tex][tex]= \sqrt{\frac{9.1 x 10^{-31} }{1.67 x 10^{-27} } } = 2.3 x 10 ^{-2}[/tex]
