6.9 The pauli exclusion principle  (Page 6/11)

Integrated Concepts

Estimate the density of a nucleus by calculating the density of a proton, taking it to be a sphere 1.2 fm in diameter. Compare your result with the value estimated in this chapter.

Integrated Concepts

The electric and magnetic forces on an electron in the CRT in [link] are supposed to be in opposite directions. Verify this by determining the direction of each force for the situation shown. Explain how you obtain the directions (that is, identify the rules used).

(a) What is the distance between the slits of a diffraction grating that produces a first-order maximum for the first Balmer line at an angle of $\text{20.0º}$ ?

(b) At what angle will the fourth line of the Balmer series appear in first order?

(c) At what angle will the second-order maximum be for the first line?

Integrated Concepts

A galaxy moving away from the earth has a speed of $\text{0.0100}c$ . What wavelength do we observe for an $n_{\text{i}}=7$ to $n_{\text{f}}=2$ transition for hydrogen in that galaxy?

Integrated Concepts

Calculate the velocity of a star moving relative to the earth if you observe a wavelength of 91.0 nm for ionized hydrogen capturing an electron directly into the lowest orbital (that is, a $n_{\text{i}}=\infty$ to $n_{\text{f}}=1$ , or a Lyman series transition).

Integrated Concepts

In a Millikan oil-drop experiment using a setup like that in [link] , a 500-V potential difference is applied to plates separated by 2.50 cm. (a) What is the mass of an oil drop having two extra electrons that is suspended motionless by the field between the plates? (b) What is the diameter of the drop, assuming it is a sphere with the density of olive oil?

Integrated Concepts

What double-slit separation would produce a first-order maximum at $3\text{.}\text{00º}$ for 25.0-keV x rays? The small answer indicates that the wave character of x rays is best determined by having them interact with very small objects such as atoms and molecules.

Integrated Concepts

In a laboratory experiment designed to duplicate Thomson’s determination of $q_e/m_e$ , a beam of electrons having a velocity of $6\text{.}\text{00}\times {\text{10}}^7\text{m/s}$ enters a $\text{5.00}\times {\text{10}}^{-3}\text{T}$ magnetic field. The beam moves perpendicular to the field in a path having a 6.80-cm radius of curvature. Determine $q_e/m_e$ from these observations, and compare the result with the known value.

Integrated Concepts

Find the value of $l$ , the orbital angular momentum quantum number, for the moon around the earth. The extremely large value obtained implies that it is impossible to tell the difference between adjacent quantized orbits for macroscopic objects.

Integrated Concepts

Particles called muons exist in cosmic rays and can be created in particle accelerators. Muons are very similar to electrons, having the same charge and spin, but they have a mass 207 times greater. When muons are captured by an atom, they orbit just like an electron but with a smaller radius, since the mass in $a_{\text{B}}=\frac{h^2}{{\mathrm{4\pi }}^2{m}_e{\text{kq}}_e^2}=\text{0.529}\times {\text{10}}^{-\text{10}}\text{m}$ is 207 $m_e$ .

(a) Calculate the radius of the $n=1$ orbit for a muon in a uranium ion ( $Z=\text{92}$ ).

(b) Compare this with the 7.5-fm radius of a uranium nucleus. Note that since the muon orbits inside the electron, it falls into a hydrogen-like orbit. Since your answer is less than the radius of the nucleus, you can see that the photons emitted as the muon falls into its lowest orbit can give information about the nucleus.