Sheet 5

Photoelectric Effect

X-rays

  1. It is required to choose a substance to operate as a photocell via the photoelectric effect using visible light (400-700)nm. Which of the following elements will do: tantalum(φ=4.2eV),tungsten(φ=4.5eV),aluminum(φ=3.2eV),barium(φ=2.5eV), or lithium(φ=2.3eV)?
  1. A satellite or an aircraft in orbit around the earth can become charged by the photoelectric effect induced by sunlight on the vehicle’s outer surface. Suppose that the satellite is coated with platinum, a metal with one of the largest work functions, φ=5.32eV. Find the longest wavelength photon that can eject a photoelectron from platinum.
  1. When monochromatic light of wavelength of 569nm shines on a potassium surface, the photoelectric current is stopped by a retarding potential of 0.99V. a) Assuming that the values of the h and e are unknown, compute the value h/e from the given data. b) Compute the work function in eV of potassium.
  1. A monochromatic beam of 400nm of very low intensity of radiation, 10-10W/m2 uniformly illuminates the cathode of a photoelectric cell which has an area of 1cm2Assuming that 1% of the incident photons produce photoelectrons that can reach the anode, calculate the current in the external circuit.
  1. The threshold wavelength for photoelectric emission in tungsten is 230nm. Calculate the wavelength of light necessary for photoelectrons with maximum kinetic energy 1.5eV to be ejected.
  1. If the work function for a metal is 1.8eV. a) What is its stopping potential for light of wavelength 400nm? b) What is the maximum speed of the emitted photoelectrons at the metal’s surface?
  1. In a photoelectric experiment in which a sodium surface is used, it is found that a stopping potential of 1.85V occurs if a wavelength of 300nm is used, and a stopping potential of 0.82V is recorded for a wavelength of 400nm. Using this data find a) a value for Planck’s constant, b) the work function of sodium, c) the cutoff wavelength of sodium.
  1. A human eye with good accommodation can detect an object if sixty or more photons/sec of visible light coming from the object entering its pupil. At what distance from the eye, which has a pupil diameter of 4mm, should a bulb radiating 100watts of 500nm light isotropically be placed such that it may be detected by the eye?
  1. Calculate the value of h/e, given that the shortest wavelength emitted by an x-ray tube operating at 20kV is equal to 6.21*10-11m.
  1. a) In an x-ray tube, the high voltage between filament and target is 105V find the shortest wavelength of photons produced by such tube.

b) What is the shortest wavelength of the x-rays emitted when accelerated electrons strike the screen of a 30kV television tube.

  1. If a 100watt light bulb emits 3% of the input energy as visible light, uniformly in all directions, approximately how many photons per second of visible light (550nm) will strike the pupil (4mm diameter) of the eye of an observer 10km away?
  1. Sunlight reaching the earth has an intensity of about 1300watt/m2. How many photons per square meter per second strike the earth? (average wavelength is 550nm) .
  1. Assume that an X-ray technician takes an average of eight X-rays per day and receives a dose of 0.0005rem/photo as a result while he stands at a distance of 50cm from the machine.Estimate:

i.the dose in rem per year if he works 5 days per week. How does the technician’s exposure compare with the minimum level of background radiation (0.13rem/yr)?

ii. at what distance would he stand to operate the machine to lower the dose to the minimum level.

Sheet 6

Atomic Line Spectra & Lasers

1.Find the wavelengths that can possibly be emitted by a H2 atom initially in the fifth state as it goes to the ground state.

2.How many of the Balmer series lines of H2 fall within the visible range (400-750) nm? Show that no lines from the Lyman and Paschen series are visible.

3.The average lifetime of an excited state of hydrogen is of the order of 10-8 . How many orbits an electron in the n=2 state will make according to according to Bohr’s model before it suffers a transition to the ground state.

4.Identify the hydrogen atom transition which results in the emission of a spectral line of wavelength 379.9 nm.

5.Calculate the difference in the wavelength between the first line of the Lyman series of ordinary H2 and that of deuterium (heavy hydrogen), given that the mass of the neutron is about two times the mass of the proton.

6.The positronium is a hydrogen-like system, with a positron replacing the proton which constitutes the hydrogen atom nucleus. The positron has the same mass as the electron, but its change is +e rather than –e.

i)Calculate the ionization energy of the positronium atom.

ii)Calculate the wavelength of the line emitted of the positronium atom in the n=2 state makes a transition to the ground state.

7.The handbook of Chemistry and Physics lists the following emission wavelengths in nm for doubly ionized Lithium : 11.39, 13.5, 54.00, 72.91. Identify these lines with the proper spectral series giving the initial state quantum number nI for each line.

8. What transition in a singly ionized helium atom He+ will emit a wavelength close to the second line in Hydrogen’s Balmer series.

9. The CO2 laser is one of the most powerfully developed lasers. The energy difference between the two laser levels is 0.117 eV. Determine the radiation emitted by this laser tube.

10.Laser action is produced by stimulated emission process. Discuss the main aspects that are achieved to increase the probability of stimulated emission over that of spontaneous absorption. How is this implemented in the He-Ne laser? What is the output frequency of this laser if transition occurs between energy levels E3 and E2 where ΔE=1.959 eV

12.The output irradiance of a diode laser source of a 1.3 refractive index, 0.3mm diameter and 1mm length is sketched to scale on Fig.(2), fo=750GHz. If it is treated as a resonant optical cavity with end reflectors, determine:

i. the number of nodes formed inside the laser active region

ii. the bandwidth of the laser output

iii. the approximate number of photons released per second

iv. the diameter of the diffraction fringe and the irradiance at a distance 100m away from the laser source.