Question

What fraction of its energy does a proton emit per second?

• A. $1.1\times {10}^{-11}{s}^{-1}$
• B. $2.1\times {10}^{-11}{s}^{-1}$
• C. $\sqrt{3}\times {10}^{-11}{s}^{-1}$
• D. $1.4\times {10}^{-11}{s}^{-1}$

Answer 1

The correct option is D $1.4\times {10}^{-11}{s}^{-1}$

We know $r=\frac{mv}{qB}$

qB = $\frac{\sqrt{2KEm}}{r}$

F = qvB = $\frac{\sqrt{2KEm}}{r}\times$ v

a = $\frac{F}{m}$ = $\frac{2KE}{mr}$

$\frac{\frac{dE}{dt}}{6Mev}=\frac{\frac{q^2{a}^2}{6\pi {ϵ}_o{c}^3}}{6Mev}$

Mass of proton is $1.6\times {10}^{-27}$ kg and charge is $1.6\times {10}^{-19}$ C

Solving the above equation with above values will give us $1.4$ x ${10}^{-11}{s}^{-1}$