The nucleus of a hydrogen atom is a single proton, which has a radius of about 1.1x 10-15 m. The single electron in a hydrogen atom orbits the nucleus at a distance of 5.3× 1011 m. What is the ratio of the density of the hydrogen nucleus to the density of the complete hydrogen atom? Number i | ! Units (no units)
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- the average density of an atom is approximately 103 kg/m3. The nucleus of an atom has a radius about 10-5 times that of the entire atom, and contains nearly all the mass of the atom. What is the approximate density, in kilograms per cubic meter, of a nucleus?Problem 13: In this problem, the symbols M, L, and T represent the dimensions mass, length, and time, respectively. Consider the physical quantities s, v, a, and t with dimensions [s] = L, [v] = LT-1, [a] = LT-2, and [t] = T. (Here, the square bracket means “the dimensions of” so, for example, [s] represents the dimensions of the quantity s.) Part (a) What is the simplest expression involving only a and s that has the same dimensions as v2? expression = ______ Part (b) What is the simplest expression involving only v and t that has the same dimensions as a? expression = ______ Part (c) What is the simplest expression involving only v and t that has the same dimensions as s? expression = ______ Part (d) What is the simplest expression involving only a and t that has the same dimensions as s? expression = ______The formula for differential volume in a spherical coordinate. a. ? sin ? ?? ?? ??b. ? sin ? ?? ?? ??c. ? sin ? ?? ?? ??d. ? sin ? ?? ?? ??
- A rectangular box with mass 16.5 g is said to have dimensions of 2.8 cm x 1.7 cm * 0.4 cm . Calculate the density of this rectangular box, in g/cm^ 3 . The volume of a rectangular box is length times width times depth (I^ * W^ * d) .The Statue of Liberty in New York City is approximately 305 ft305 ft tall. How many U.S. dimes would be in a stack of the same height? Each dime is 1.35 mm1.35 mm thick. number of dimes: Each dime has a mass of 2.268 g.2.268 g. How much would the stack of dimes from the previous question weigh? mass: g What is the value, in dollars, of the same stack of dimes? value: dollars The 2017 U.S. gross domestic product (GDP) was valued at 19,390,604,000 dollars.19,390,604,000 dollars. How many Statue of Liberty‑height stacks of dimes are needed to match the GDP in value? number of stacks:You are making a sculpture that is a pyramid with a square base . You want the height of the pyramid to be 4 inches less than the length of a side of the base . You want the volume of the sculpture to be 200 cubic inches . a . Let x represent the length ( in inches ) of a side of the sculpture's base . Draw a diagram of the sculpture , and label the dimensions in terms of x . b . Write a function that gives the volume V of the sculpture in terms of x .
- A rectangle expands and contracts with time t (in seconds). Its area is given by A= 4 + sin t square meters. At t = 3.14 (pi), the following is observed. (1) the width of the rectangle expands at the rate of 0.1 meters per second. (2) The width of the rectangle is 1 meter long How fast is the height of the rectangle changing at t = 3.14 (pi)?What was the error in the following measurements? Mass (kg) Volume(m^3) Density (kg/m^3) 1.16 0.001 1160 2.46 0.0023 1069.565217 5.16 0.005 1032 10.16 0.01 1016 13.66 0.0135 1011.851852 There was no error in measurement There was a random error in the measurement of volume. The mass was measured with a systematic error Human error