The nearest star to our sun is Proxima Centauri, at a distance of 4.3 light-years from the sun. A light-year is the distance that light travels in one year (365 days). How far away, in km, is Proxima Centauri from the sun?

List these types of electromagnetic radiation in order of (ii) increasing energy per photon. a. radio waves b. microwaves c. infrared radiation d. ultraviolet radiation

List these types of electromagnetic radiation in order of (i) increasing frequency and (ii) decreasing energy per photon. a. gamma rays b. radio waves c. microwaves d. visible light

Calculate the energy of a photon of electromagnetic radiation at each of the wavelengths indicated in Problem 39. a. 632.8 nm (wavelength of red light from helium–neon laser) b. 503 nm (wavelength of maximum solar radiation) c. 0.052 nm (wavelength contained in medical X-rays)

A laser pulse with wavelength 532 nm contains 3.85 mJ of energy. How many photons are in the laser pulse?

A heat lamp produces 32.8 watts of power at a wavelength of 6.5 µm. How many photons are emitted per second? (1 watt = 1 J/s)

Determine the energy of 1 mol of photons for each kind of light. (Assume three significant figures.) a. infrared radiation (1500 nm) b. visible light (500 nm) c. ultraviolet radiation (150 nm)

How much energy is contained in 1 mol of each? a. X-ray photons with a wavelength of 0.135 nm b. γ-ray photons with a wavelength of 2.15×10^–5 nm

Sketch the interference pattern that results from the diffraction of electrons passing through two closely spaced slits.

The resolution limit of a microscope is roughly equal to the wavelength of light used in producing the image. Electron microscopes use an electron beam (in place of photons) to produce much higher resolution images, about 0.20 nm in modern instruments. Assuming that the resolution of an electron microscope is equal to the de Broglie wavelength of the electrons used, to what speed must the electrons be accelerated to obtain a resolution of 0.20 nm?

The smallest atoms can themselves exhibit quantum-mechanical behavior. Calculate the de Broglie wavelength (in pm) of a hydrogen atom traveling at 475 m/s.

A proton in a linear accelerator has a de Broglie wavelength of 122 pm. What is the speed of the proton?

A 0.22-caliber handgun fires a 1.9-g bullet at a velocity of 765 m/s. Calculate the de Broglie wavelength of the bullet. Is the wave nature of matter significant for bullets?

An electron traveling at 3.7×10⁵ m/s has an uncertainty in its velocity of 1.88×10⁵ m/s. What is the uncertainty in its position?

What are the possible values of l for each given value of n? a. 1 b. 2 c. 3 d. 4

What are the possible values of m_l for each value of l? a. 0

What are the possible values of m_l for each value of l? b. 1

What are the possible values of m_l for each value of l? c. 2 d. 3

Which set of quantum numbers cannot occur together to specify an orbital? a. n = 2, l = 1, m_l = -1 b. n = 3, l = 2, m_l = 0 c. n = 3, l = 3, m_l = 2 d. n = 4, l = 3, m_l = 0

Which combinations of n and l represent real orbitals, and which do not exist? a. 1s b. 2p c. 4s d. 2d

Sketch the 1s and 2p orbitals. How do the 2s and 3p orbitals differ from the 1s and 2p orbitals?

Determine whether each transition in the hydrogen atom corresponds to absorption or emission of energy. a. n = 3 → n = 1 b. n = 2 → n = 4 c. n = 4 → n = 3

According to the quantum-mechanical model for the hydrogen atom, which electron transition produces light with the longer wavelength: 3p → 2s or 4p → 3p?

Calculate the frequency of the light emitted when an electron in a hydrogen atom makes each transition: a. n = 4 → n = 3 b. n = 5 → n = 1 c. n = 5 → n = 4 d. n = 6 → n = 5

An electron in the n = 7 level of the hydrogen atom relaxes to a lower-energy level, emitting light of 397 nm. What is the value of n for the level to which the electron relaxed?