calculations of protons

Mar 2020
11
1
KA
Information:
Mass of proton:\(\displaystyle 1.67×10^−27kg\)

Mass of electron: \(\displaystyle 9.11×10^−31kg\)

Proton charge \(\displaystyle +1.60×10^-19 C\)

Question:


A proton is accelerated through a voltage of 248 kV.

a) Calculate the energy of the proton in electron volt and in Joule.

b) Assuming that the mass of the proton remains the same as its rest mass, calculate the speed of the photon.

c)The proton is curved by a magnetic field of 1.5 Telsa. Calculate the radius of the curvature of its path.

My workings:

a) is 248keV.
\(\displaystyle 3.97*10^{−14 }J.\)

b) v = √(2K/m)
\(\displaystyle √(2*3.97*10^{-14})/1.67*10^{-27}) = 6.89354 * 10^6 ms^-1 \)


c) r = mv/(eB) r=\(\displaystyle 1.67*10^{-19}* 6.89354 *10^6/(1.60*10^{-19}*1.5) = 4.8 * 10^6 m\)

Have I done these correctly?
 
Mar 2020
11
1
KA
(a) and (b) are ok

check the mass value of the proton you used in part (c)
\(\displaystyle (1.67∗10^-27∗6.89354∗10^6)/(1.60∗10^−19∗1.5)=0.048\) is it nm or m?
 

skeeter

Math Team
Jul 2011
3,355
1,848
Texas
\(\displaystyle (1.67∗10^-27∗6.89354∗10^6)/(1.60∗10^−19∗1.5)=0.048\) is it nm or m?
do a dimensional analysis

$\dfrac{mv}{qB} = \dfrac{(kq)(m/s)}{(C)(T)}$

what are the SI units for a Tesla?
 
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skeeter

Math Team
Jul 2011
3,355
1,848
Texas
You trust your calculator?
 

skeeter

Math Team
Jul 2011
3,355
1,848
Texas
if you entered the values as you typed in post #3, you're good to go
 
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