The electric force of repulsion between two electrons is similar to the gravitational force: where k is called Planck's constant, q is the charge on a particle, and r is the distance separating the charges. Find the new force of repulsion between them, in terms of R: a. when the distance between the electrons is doubled. b, when the distance between the electrons is multiplied by 1.2. C. when the distance between the electrons is multiplied by 1/3. D. when the distance between the electrons is divided by 6.

A marathon runner completes a 42.188-km course in 2 h, 30 min, and 12 s. There is an uncertainty of 25 m in the distance traveled and an uncertainty of 1 s in the elapsed time. (a) Calculate the percent uncertainty in the distance. (b) Calculate the uncertainty in the elapsed time. (c) What is the average speed in meters per second? (d) What is the uncertainty in the average speed?

Suppose a star 1000 times brighter than our Sun (that is, emitting 1000 times the power) suddenly goes supernova. Using data from Table 7.3: (a) By what factor does its power output increase? (b) How many times brighter than our entire Milky Way galaxy is the supernova? (c) Based on your answers, discuss whether it should be possible to observe supernovas in distant galaxies. Note that there are on the order of 1011 observable galaxies, the average brightness of which is somewhat less than our own galaxy.

Calculate the approximate number of atoms in a bacterium. Assume that the average mass of an atom in the bacterium is ten times the mass of a hydrogen atom. (Hint: The mass of a hydrogen atom is on the order of 10-27 kg and the mass of a bacterium is on the order of 10-15 kg.) Figure 1.28 This color-enhanced photo shows Salmonella typhimurium (red) attacking human cells. These bacteria are commonly known for causing foodborne illness. Can you estimate the number of atoms in each bacterium? (credit: Rocky Mountain Laboratories, NIAID, NIH)

(a) Calculate the wavelength of a photon that has the same momentum as a proton moving at 1.00% of the speed of light. (b) What is the energy of the photon in MeV? (c) What is the kinetic energy of the proton in MeV?

The sun energy at a rate of 3.85×10 26 W by the fusion of hydrogen. About 0.7% of each kilogram of hydrogen goes into the energy generated by the Sun. (a) How many kilograms of hydrogen undergo fusion each second? (b) If the sun is 90.0% hydrogen and half of this can undergo fusion before the sun changes character, how long could it produce energy at its current rate? (c) How many kilograms of mass is the sun losing per second? (d) What fraction of its mass will it have lost in the time found in part (b)?

(a) A -ray photon has a momentum of 8.001021kgm/s. What is its wavelength? (b) Calculate its energy in MeV.

What is wrong with the following expressions? How can you correct them? (a) C=AB , (b) C=AB , (c) C=AB , (d) C=AB , (e) C+2A=B , (f) C=AB , (g) AB=AB , (h) C=2AB , (i) C=A/B , and (j) C=A/B .

Raymond Davis Jr.’s neutrino detector contained approximately 1030 chlorine atoms. During his experiment, he found that one neutrino reacted with a chlorine atom to produce one argon atom each day. A. How many days would he have to run the experiment for 1% of his tank to be filled with argon atoms? B. Convert your answer from A. into years. C. Compare this answer to the age of the universe, which is approximately 14 billion years (1.41010y) . D. What does this tell you about how frequently neutrinos interact with matter?

How does a model differ from a theory?