In cancer treatments, proton therapy is one type of radiation therapy used. In p

Question

In cancer treatments, proton therapy is one type of radiation therapy used. In proton therapy, hydrogen atoms are separated into protons and electrons. The protons are then accelerated in an electric field to achieve a kinetic energy of 70 to 250 million electron volts. What is the de Broglie wavelength for a proton that has a kinetic energy of 70 million electron volts? Hints: 1eV = 1.602x10-19J and the relationship between kinetic energy and velocity is KE = 1/2mv2.

Please show your work and the formulas you used. I'm really just making sure I used the correct formulas properly.

Explanation / Answer

=h/(mv)

mass of proton= 1.67*10^-27 kg

Ek = 80*10^6 eV

Factor --> 1.6*10^-19 J/eV

Ek = 1.28*10^-11 J

KE = 1/2mv2.

Solve for v

V = sqrt(2Ek/m) = sqrt((2*1.28*10^-11 J)/(1.67*10^-27 kg)) = 1.24*10^8 m/s

For Broglie:

=h/(mv)

h = 6.63*10^-34 Js

m = 1.67*10^-27 kg

v = 1.24*10^8 m/s

Susbtitute all

=h/(mv) = 6.63*10^-34 Js / (1.67*10^-27 kg * 1.24*10^8 m/s) = 32.01 m

thats the wavelenght

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