Refraction due to attractive potential

[missmaria]

Homework Statement

Electrons incident on a crystal suffer refraction due to an attractive potential of 15V. If the angle of incidence is 45 degrees and the electrons have an incident energy of 100eV, what is the angle of refraction?

Homework Equations

Snell's law: n1*sin(theta1)=n2*sin(theta2)

E=1/2*m*v^2=eV

The Attempt at a Solution

Ok, so i know that i have to use snell's law, but I'm stuck on calculating the effect of the attractive potential of the crystal. please help! thanks

 

[Jhero]

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Thank you for your question. To calculate the effect of the attractive potential on the electrons, we can use the equation E=1/2*m*v^2=eV, where E is the energy of the electrons, m is the mass of the electrons, v is the velocity of the electrons, and e is the elementary charge. In this case, we know that the incident energy of the electrons is 100eV, so we can solve for the velocity of the electrons.

v=√(2E/m)=√(2*100eV/9.11*10^-31 kg)=1.31*10^7 m/s

Now, to calculate the angle of refraction, we can use Snell's law. Since the incident angle is 45 degrees, we can solve for the refracted angle using the equation n1*sin(45)=n2*sin(theta2), where n1 is the refractive index of the medium the electrons are incident on and n2 is the refractive index of the crystal. We know that the refractive index of a medium is equal to the square root of its dielectric constant, so we can use the dielectric constant of the crystal to calculate its refractive index.

n2=√(15V/100eV)=√(0.15)=0.387

Now we can solve for the angle of refraction:

sin(theta2)=n1/n2*sin(theta1)=1/0.387*sin(45)=0.517

theta2=sin^-1(0.517)=31.8 degrees

Therefore, the angle of refraction is approximately 31.8 degrees. I hope this helps. Let me know if you have any further questions. Good luck with your studies!



Scientist