Estimate the average mass density of a sodium atom assuming its size to be about 2.5 Å. (Use the known values of Avogadro’s number and the atomic mass of sodium). Compare it with the density of sodium in its crystalline phase : 970 kg m–3. Are the two densities of the same order of magnitude ? If so, why ?
Diameter of sodium atom = Size of sodium atom = 2.5 Å
Radius of sodium atom, r = 1/2 x 2.5 Å = 1.25 Å
= 1.25 × 10-10 m
Volume of sodium atom, V = 4/3 πr3
= 4/3 x 22/7 x (1.25 × 10-10) 3
According to the Avogadro hypothesis, one mole of sodium contains 6.023 × 1023 atoms and has a mass of 23 g or 23 × 10-3 kg.
∴ Mass of one atom = 23 × 10-3 / 6.023 x 10-3 kg
Density of sodium atom, p = 
It is given that the density of sodium in crystalline phase is 970 kg m-3.
Hence, the density of sodium atom and the density of sodium in its crystalline phase are not in the same order. This is because in solid phase, atoms are closely packed. Thus, the inter-atomic separation is very small in the crystalline phase.
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State the number of significant figures in the following:
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Fill in the blanks by suitable conversion of units:
(a) 1 kg m2s–2= ....g cm2 s–2
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A physical quantity P is related to four observables a, b, c and d as follows :
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(e) a high-speed electron in space far from all material objects, and free of electric and magnetic fields. - Q:-
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On an open ground, a motorist follows a track that turns to his left by an angle of 60° after every 500 m. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.
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(b) a monkey sitting on top of a man cycling smoothly on a circular track.
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(d) a tumbling beaker that has slipped off the edge of a table. - Q:-
A transverse harmonic wave on a string is described by
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Where x and y are in cm and t in s. The positive direction of x is from left to right.
(a) Is this a travelling wave or a stationary wave? If it is travelling, what are the speed and direction of its propagation?
(b) What are its amplitude and frequency?
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The principle of ‘parallax’ in section 2.3.1 is used in the determination of distances of very distant stars. The baseline AB is the line joining the Earth’s two locations six months apart in its orbit around the Sun. That is, the baseline is about the diameter of the Earth’s orbit ≈ 3 × 1011m. However, even the nearest stars are so distant that with such a long baseline, they show parallax only of the order of 1” (second) of arc or so. A parsec is a convenient unit of length on the astronomical scale. It is the distance of an object that will show a parallax of 1” (second) of arc from opposite ends of a baseline equal to the distance from the Earth to the Sun. How much is a parsec in terms of metres ?
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A transverse harmonic wave on a string is described by
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The mass of a box measured by a grocer's balance is 2.300 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. What is
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In changing the state of a gas adiabatically from an equilibrium state A to another equilibrium state B, an amount of work equal to 22.3 J is done on the system. If the gas is taken from state A to B via a process in which the net heat absorbed by the system is 9.35 cal, how much is the net work done by the system in the latter case? (Take 1 cal = 4.19 J)
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A metre long narrow bore held horizontally (and closed at one end) contains a 76 cm long mercury thread, which traps a 15 cm column of air. What happens if the tube is held vertically with the open end at the bottom?
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