BackA scientist has devised a new method of isolating individual particles. He claims that this method enables him to detect simultaneously the position of a particle along an axis with a standard deviation of nm and its momentum component along this axis with a standard deviation of kg-m/s. Use the Heisenberg uncertainty principle to evaluate the validity of this claim.
The star Alpha goes supernova. Ten years later and 100 ly away, as measured by astronomers in the galaxy, star Beta explodes. An alien spacecraft passing through the galaxy finds that the distance between the two explosions is 120 ly. According to the aliens, what is the time between the explosions?
Two events in reference frame S occur 10 μs apart at the same point in space. The distance between the two events is 2400 m in reference frame S'. What is the velocity of S' relative to S?
FIGURE P39.31 shows the wave function of a particle confined between x = 0 nm and x = 1.0 nm. The wave function is zero outside this region. Calculate the probability of finding the particle in the interval 0 nm ≤ x ≤ 0.25 nm.
What minimum bandwidth is needed to transmit a pulse that consists of 100 cycles of a 1.0 MHz oscillation?
FIGURE EX39.13 shows the probability density for an electron that has passed through an experimental apparatus. What is the probability that the electron will land in a 0.010-mm-wide strip at x = 0.000 mm?
What quantum number of the hydrogen atom comes closest to giving a 100-nm-diameter electron orbit?
In a set of experiments on a hypothetical one-electron atom, you measure the wavelengths of the photons emitted from transitions ending in the ground level (), as shown in the energy-level diagram in Fig. E. You also observe that it takes eV to ionize this atom. What is the energy of the atom in each of the levels (, , etc.) shown in the figure?
It might seem strange that in beta decay the positive proton, which is repelled by the positive nucleus, remains in the nucleus while the negative electron, which is attracted to the nucleus, is ejected. To understand beta decay, let's analyze the decay of a free neutron that is at rest in the laboratory. We'll ignore the antineutrino and consider the decay n → p⁺ + e⁻. The analysis requires the use of relativistic energy and momentum, from Chapter 36. Write the equation that expresses the conservation of relativistic momentum for this decay. Let v represent speed, rather than velocity, then write any minus signs explicitly.
A sample of 1.0 x 1010 atoms that decay by alpha emission has a half-life of 100 min. How many alpha particles are emitted between t = 50 min and t = 200 min?
When 5×1012 photons pass through an experimental apparatus, 2.0×109 land in a 0.10-mm-wide strip. What is the probability density at this point?
In one experiment, 2000 photons are detected in a 0.10-mm-wide strip where the amplitude of the electromagnetic wave is 10 V/m. How many photons are detected in a nearby 0.10-mm-wide strip where the amplitude is 30 V/m?
A proton is in a box of width . What must the width of the box be for the ground-level energy to be MeV, a typical value for the energy with which the particles in a nucleus are bound? Compare your result to the size of a nucleus — that is, on the order of m.
(II) What is the speed of an electron after being accelerated from rest by 28,000 V?
The uncertainty in the y-component of a proton's position is m. What is the minimum uncertainty in a simultaneous measurement of the -component of the proton's velocity?