Question

1.1 Suppose you want to make a scale model of a hydrogen atom. You choose, for the nucleus, a small ball bearing with a radius of [01] mm. The radius of the hydrogen atom is 0.529 × 10−10 m and the radius of the nucleus is 1.2 × 10−15 m. (a) What would be the radius (m) of the model? (b) Suppose that now you want to make a scale model of the solar system using the same ball bearing as in part (a) to represent the sun. How far from it (mm) would you place a sphere representing the earth? (Center to center distance please.) (See the inside cover of your textbook for data.) (c) What would be the radius (mm) of the sphere representing the earth in part (b)?

1.2. (a) Atoms are typically spaced about 0.2 nm apart. At that spacing, how many atoms would be found in a line [02] inches long? Enter your answer to 2 significant figures. (b) A water molecule has a mass of 3.0 × 10−26 kg. Assuming the molecules have the spacing given above, about how many kg of water are in [03] cubic inches (in3 )? (Don’t expect this number to be accurate. The number given part (a) is very rough.)

1.3. Mathematical functions, such as trigonometric functions and exponential functions, produce answers that are pure numbers. Consider the following formula: x = A cos(Bt2 ). “x” is in meters and “t” is in seconds. Which of the following must be the units of A? 1/m, m/rad, m/s2 , m, m/s.

1.4. Trigonometric functions take an angular unit as their argument. Consider the following formula: x = A cos(Bt2 ). “x” is in meters and “t” is in seconds. Which one of the following is the least acceptable units for B? degree/s2 , m/s2 , radian/s2 , revolution/s2 . 1.5. How many significant figures are in the following numbers? (a) 7 (b) 6.478 × 1012 (c) 0.700 (d) 0.0004

Answer 1

1.1b) The distance between sun and earth on this scale = 0.214m = 214 mm

1.1c) The radius of earth on this scale = 9.15*10^-6 = 915*10^-3 mm

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