ZCT104/3 MODERN PHYSICS ASSIGNMENT 3 2022

Questions

Marks

de Broglie’s Wavelength

1. An electron has a de Broglie wavelength of 2.00 pm. Find the kinetic energy (K), phase velocity (n_p) and group velocity (n_g) of its de Broglie waves.

2. Solve the de Broglie wavelength of:

a. a tennis ball of mass 57 g traveling 25 m/s

b. an electron with kinetic energy 50 eV.

3. Find the de Broglie wavelength of a 1.00-MeV proton. Is a relativistic calculation needed?

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Experimental Evidence

4. A beam of 50-keV electrons is directed at a crystal and diffracted electrons are found at an angle of 50° relative to the original beam. What is the spacing of the atomic planes of the crystal? Is relativistic calculation needed for l.

5. The Bragg condition is sin q = nλ/D. The 350 eV electron beam is nonrelativistic. What is the de Broglie wavelength? What is the value of q when n= 1,2, 3 and 4? (Given: d-spacing is 0.315nm).

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Heisenberg Uncertainty Principle

6. The kinetic energy of a non-relativistic particle in terms of its momentum can be written as K= p²/2m. Estimate the minimum kinetic energy (in eV) of a proton confined within a nucleus having a diameter of 1 fm (1 fm = 10^-15 m).

7. (a)    How much time is needed to measure the kinetic energy of an electron whose     

        speed is 10.0 m/s with an uncertainty of no more than 0.100 percent? How

        far will the electron have travelled in this period of time?

(b)   Make the same calculations as in (a) for a 1.00-g insect whose speed is the

        same. What do these sets of figures indicate?

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Conclusion

Build a mind map to conclude Chapter 4 : The Wave-like Properties of Particles.

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