Instead of the arrangement in
, the speed of molecules can also be measured with a rotating slotted-
disc apparatus, which consists of five coaxial 5.0 cm diameter discs separated by 1.0 cm, the slots in their rims
being displaced by 2.0° between neighbours. The relative intensities,
, of the detected beam of Kr atoms for two
different temperatures and at a series of rotation rates were as follows:
Find the distributions of molecular velocities,
),at these temperatures, and check that they conform to the
theoretical prediction for a one-dimensional system.
Cars were timed by police radar as they passed in both directions below a bridge. Their velocities (kilometres
per hour, numbers of cars in parentheses) to the east and west were as follows: 80 E (40), 85 E (62), 90 E (53), 95
E (12), 100 E (2); 80 W (38), 85 W (59), 90 W (50), 95 W (10), 100 W (2). What are (a) the mean velocity, (b) the
mean speed, (c) the root mean square speed?
A population consists of people of the following heights (in metres, numbers of individuals in brackets): 1.80
(1), 1.82 (2), 1.84 (4), 1.86 (7), 1.88 (10), 1.90 (15), 1.92 (9), 1.94 (4), 1.96 (0), 1.98 (1). What are (a) the mean
height, (b) the root mean square height of the population?
Calculate the ratio of the thermal conductivities of gaseous hydrogen at 300 K to gaseous hydrogen at 10 K.
Be circumspect, and think about the modes of motion that are thermally active at the two temperatures.
A Knudsen cell was used to determine the
of germanium at 1000°C. During an interval of
7200 s the mass loss through a hole of radius 0.50 mm amounted to 43
g. What is the
germanium at 1000°C? Assume the
to be monatomic.
Bk (berkelium) decays by producing
particles, which capture electrons and form He atoms. Its
half-life is 4.4 h. A sample of mass 1.0 mg was placed in a container of volume 1.0 cm
that was impermeable to
radiation, but there was also a hole of radius 2.0
m in the wall. What is the pressure of helium at 298 K, inside the
container after (a) 1.0 h, (b) 10 h?
An atomic beam is designed to function with (a) cadmium, (b) mercury. The source is an oven maintained at
380 K, there being a small slit of dimensions 1.0 cm × 1.0 × 10
cm. The vapour pressure of cadmium is 0.13 Pa
and that of mercury is 12 Pa at this temperature. What is the atomic current (the number of atoms per unit time) in