Dozens of intermediate to advanced posts on physics have appeared over the years since I began this blog. They range from basic atomic physics, e.g.

To theoretical mechanics, e.g.

__no more than 30 minutes__, max):

1. The photo-electric threshold of tungsten is 2300A (where A denotes Angstrom). Estimate the energy E of the electrons ejected from the surface by ultraviolet light of wavelength 1800A.

2. Find the minimum energy in electron volts (eV) for an electron in a spark discharge to strip a sodium (Na) atom (Z = 11) of its last electron, assuming the other ten are already removed.

3. Let **r^** be a position vector. Then find the divergence of **r^.**

4. Let **r^** be a position vector and ** a **be a constant vector. Then find the gradient of the scalar product:

*****

*a***r^.**

5. Consider the matrix:

(0........0........1)

(0........1.........0)

(1.........0 .......0)

a) Find Tr, the trace of the matrix

b) Find the eigenvalues of the matrix.

6. Let U1 and U2 be orthonormal functions. Find the value of N which normalizes:

F = N(U1 + 2i(U2)

7. Two men together support a uniform plank of wood. At the instant one of the men lets go of his end, what is the force the other man feels?

**Questions 8-9:**

Consider two coordinate systems whose origins are non-accelerating. Assume that one of these systems (denoted by primes) is rotating with constant angular velocity w with respect to the other which is non-rotating. (Let** i'** be one of three orthogonal unit vectors in the rotating system)

8. Find the time derivative in the non-rotating system.

9. Find the second order time derivative in the non-rotating system.

10. If two strings, whose densities are 25 g/cm and 9 g/cm are joined together then find the reflection coefficient for the vibration waves.

11. A particle of mass m moves in a plane under the influence of a force F = - kr directed toward the origin. Show a polar coordinate system (r, theta) to describe the motion of the particle and thence or otherwise give the **Lagrangian** for the system.

12. According to relativistic mechanics the actual velocity of the electrons whose kinetic energy is 0.25Mev is what?

13. Compute the effective mass of a photon of wavelength 6000 A using the Einstein mass-energy equation.** Questions 14 and 15**:

When the Sun is directly overhead, a given square meter surface of the Earth receives about 1300 watts of radiant energy. Assume this energy is in the form of a plane-polarized monochromatic wave.

14. Find the rms (root mean square) magnitude of the electric field of the wave.

15. Find the rms magnitude of the magnetic field for the wave.

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