Thermal Physics, Waves, Optics and Modern Physics for the Olympiad — Practice

Question 1

Light of wavelength 250 nm falls on a metal of work function 2.0 eV. Find the maximum kinetic energy.

Accepted Answer

E = 1240/250 = 4.96 eV, so K = 2.96 eV.

Question 2

A sample has a half-life of 8 days. What fraction remains after 24 days?

Accepted Answer

Three half-lives, so one-eighth.

Question 3

A monatomic ideal gas is compressed adiabatically to half its volume. Find T2/T1.

Accepted Answer

T2/T1 = 2^(2/3) = 1.59.

Question 4

A string of length 0.8 m, tension 100 N and linear density 0.01 kg/m is fixed at both ends. Find the fundamental frequency.

Accepted Answer

v = root(100/0.01) = 100 m/s, so f1 = 100/(2 x 0.8) = 62.5 Hz.

Question 5

In Young's experiment lambda = 600 nm, D = 1 m and d = 1 mm. Find the fringe width.

Accepted Answer

beta = lambda D/d = 0.6 mm.

Question 6

Find the wavelength of the n = 3 to n = 2 transition in hydrogen.

Accepted Answer

Energy = 13.6(1/4 - 1/9) = 1.89 eV, so wavelength = 1240/1.89 = 656 nm.

Question 7

A clock moving at 0.6c records 1 microsecond. How long does the lab observe?

Accepted Answer

gamma = 1.25, so the lab measures 1.25 microseconds.

Question 8

Which harmonics does an air column closed at one end support?

Accepted Answer

Only odd harmonics: f = n v/(4L) for odd n.

Practice — Thermal Physics, Waves, Optics and Modern Physics for the Olympiad