Solving Electron Acceleration and Reflection Problems

[hayowazzup]

Homework Statement

Electrons are accelerated from rest by a voltage of 59.0 V. After that acceleration:
1.What is their speed?
2.What is their De Broglie wavelength?
3.The accelerated electrons are then reflected by a crystal with crystal spacing d of 0.085 nm. Through which angle are they reflected?

h = 6.63 × 10–34 J.s, c = 3 × 108 m/s, Mass of e = 9.11 × 10–31 kg, e = 1.6 × 10–19 C.

Homework Equations

The Attempt at a Solution

1. √((2*e*V)/massofe) = √((2*1.6 × 10–19 *59)/9.11 × 10–31 ) = 4552414.59 m/s
2. λ = h/p = h / √(2*h*e*massofe) = 6.63 × 10–34 / √((2*1.6 × 10–19 * 9.11 × 10–31 ) * (1E-9) = 0.16 nm
3. 2dsin (θ) = m λ
= sin-1 (1* 0.16 / (2 * 0.085)) = 70 ...<=== i m stuck because the answer in the book is 39.8
i really need help

 

[Jhero]

Hello! I can help you with your questions.

1. Your calculation for the speed of the electrons is correct. However, it is given in m/s, not in nm/s. So the correct answer would be 4.55 x 10^6 m/s.

2. Your calculation for the De Broglie wavelength is also correct. However, the crystal spacing is given in nm, so the wavelength should also be in nm. Therefore, the correct answer would be 0.16 nm.

3. The formula you used for the angle of reflection is correct, but you made a mistake in your calculation. The angle of reflection should be in radians, not degrees. So the correct calculation would be sin-1 (1* 0.16 / (2 * 0.085)) = 0.78 radians. To convert this to degrees, you can multiply by 180/π, which gives an angle of 44.7 degrees. This is closer to the answer given in the book (39.8 degrees) but may still be slightly off due to rounding errors.

I hope this helps! Let me know if you have any other questions or need further clarification.