BackThere exist subatomic particles whose spin is characterized by s = 1, rather than the s = ½ of electrons. These particles are said to have a spin of one. What is the magnitude ( as a multiple of ℏ ) of the spin angular momentum S for a particle with a spin of one?
A hydrogen atom in its fourth excited state emits a photon with a wavelength of 1282 nm. What is the atom's maximum possible orbital angular momentum (as a multiple of ℏ ) after the emission?
Prove that the normalization constant of the 2p radial wave function of the hydrogen atom is (24πaB3)-1/2, as shown in Equations 41.7. Hint: See the hint in Problem 32.
A sodium atom emits a photon with wavelength 818 nm shortly after being struck by an electron. What minimum speed did the electron have before the collision?
Suppose you put five electrons into a 0.50-nm-wide one-dimensional rigid box (i.e., an infinite potential well). What is the ground-state energy—that is, the total energy of all five electrons in the ground-state configuration?
During what interval of time will 10% of a sample of 2p hydrogen atoms decay?
A ruby laser emits a 100 MW, 10-ns-long pulse of light with a wavelength of 690 nm. How many chromium atoms undergo stimulated emission to generate this pulse?
A classical atom that has an electron orbiting at frequency ⨍ would emit electromagnetic waves of frequency ⨍ because the electron's orbit, seen edge-on, looks like an oscillating electric dipole. What is the total mechanical energy of this atom?
Physicists first attempted to understand the hydrogen atom by applying the laws of classical physics. Consider an electron of mass m and charge −e in a circular orbit of radius r around a proton of charge +e. Use Newtonian physics to show that the total energy of the atom is E =−e²/8πϵ₀𝓇
Physicists first attempted to understand the hydrogen atom by applying the laws of classical physics. Consider an electron of mass m and charge −e in a circular orbit of radius r around a proton of charge +e. The minimum energy needed to ionize a hydrogen atom (i.e., to remove the electron) is found experimentally to be 13.6 eV. From this information, what are the electron's speed and the radius of its orbit?
Identify the unknown isotope in the following decays.
The radium isotope ²²³Ra, an alpha emitter, has a half-life of 11.43 days. You happen to have a 1.0 g cube of ²²³Ra, so you decide to use it to boil water for tea. You fill a well-insulated container with 100 mL of water at 18℃ and drop in the cube of radium. How long will it take the water to boil?
There is evidence that low-energy x rays have an RBE slightly greater than 1. Suppose that 10 keV photons with an RBE of 1.2 are used to make a chest x ray. A 60 kg person receives a 0.30 mSv dose from a chest x ray that exposes 25% of the patient's body. How many x ray photons are absorbed in the patient's body?
All the very heavy atoms found in the earth were created long ago by nuclear fusion reactions in a supernova, an exploding star. The debris spewed out by the supernova later coalesced into the gases from which the sun and the planets of our solar system were formed. Nuclear physics suggests that the uranium isotopes ²³⁵U and ²³⁸U should have been created in roughly equal numbers. Today, 99.28% of uranium is ²³⁸U and only 0.72% is ²³⁵U. How long ago did the supernova occur?
To initiate a nuclear reaction, an experimental nuclear physicist wants to shoot a proton into a 5.50-fm-diameter ¹²C nucleus. The proton must impact the nucleus with a kinetic energy of 3.00 MeV. Assume the nucleus remains at rest. Through what potential difference must the proton be accelerated from rest to acquire this speed?