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. : "Modern Physics"

Modern Physics: Hydrogen Atom

Q- An electron orbiting a hydrogen atom has an initial energy of -0.544 eV. The atom emits a photon, then absorbs a photon, ending up with an energy of -3.4 eV. What was the wavelength of the emitted photon?

Solution:

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Quantum Physics: Potential Well

Q- An electron is trapped in an infinite well of width 11 nm. If the electron drops down 5 energy levels and, in the process, emits a photon with wavelength 642.94 nm, then what is the final energy of the electron?

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Hydrogen (Like) Atom

Q- The first three energy levels of the fictitious element X are E1 = -3.8 eV, E2 = -1.7 eV, and E3 = -1.2 eV. Element X has one electron in the ground state.

(a) What is the ionization energy of element X?

(b) Calculate the (i) shortest and (ii) next-shortest wavelengths observed in the absorpti…

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Photoelectric Effect

Q- The measurements of a photoelectric-effect experiment are graphed in in Figure, in which the intervals along the horizontal and vertical axes are respectively given by 5.9*1014 Hz and 2.50 V, respectively.

(a) What is the work function of the cathode?

(b) What experimental value of Planck's con…

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Photo Electric Effect

Q-The maximum kinetic energy of photoelectrons is 2.8 eV. When the wavelength of the light is increased by 50%, the maximum energy decreases to 1.3 eV. What are the following quantities?

(a) The work function of the cathode

(b) The initial wavelength

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Modern Physics

Q- A 150 W light bulb emits about 8 W of visible light. (The other 142 W are emitted as infrared radiation or lost as heat to the surroundings.) The average wavelength of the visible light is about 510 nm, so make the simplifying assumption that all the visible light has this wavelength.

(a) What i…

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Modern Physics: Photoelectric Effect

Q- A photoelectric-effect experiment finds a stopping potential of 1.9 V when light of 295 nm is used to illuminate the cathode.

(a) What is the work function of the metal used to made cathode? 

(b) What is the stopping potential if the intensity of the light is doubled?

Solution:

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Modern Physics: Radioactivity

Q- A drug tagged with a radioactive tracer (half life = 6.05 hours) is prepared for a patient.

(a) What is the decay constant for the radioactive tracer?

(b) If the initial mass of the radioactive tracer is 1g, what mass of it will remain after 24 hours?

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Modern Physics: Absorption of Gamma Rays

Q- A collimated gamma ray beam consists of equal numbers of 0.1 MeV and 1.0 MeV photons. If the beam enters a 15 cm thick concrete shield, what is the relative portion of 1 MeV photons to 0.1 MeV photons in the emergent beam? 

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Photo Electric Effect

Q- An ultraviolet photon with wavelength 172 nm strikes an aluminum surface with a work function φ = 3.87 eV and ejects an electron. What is the shortest wavelength λ that can be observed for the ejected electron?

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Matter Waves: de Broglie Wavelength

Q- Electrons with a speed of 2.5 *106 m/s pass through a double-slit apparatus. Interference fringes are detected with a fringe spacing of 1.6 mm.

(a) What will the fringe spacing be if the electrons are replaced by neutrons with the same speed?

(b) What speed must neutrons have to produce interfe…

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Radiation Pressure

Q- Calculate the work done on a 1000 square meter, 1 kg solar sail during a trip from Earth to Mars. Assume the sunlight is normal to the sail during the trip and is totally reflective. Consider forces of gravity of the sun and its radiation pressure only. 

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Hydrogen Like Atom

Q- An electron in Chromium (Z=24) moves from the n=2 to the n=1 state without emitting a photon. Instead, the excess energy is transmitted to an outer electron (n=4 state), which is emitted. This is called an Auger Electron. Using ionization considerations, calculate the kinetic energy of the Auger …

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Photo Electric Effect

Q- Light from a laser hits the surface of cesium, with minimum photon energy of 2.5 eV being required to remove photons. When the surface of cesium is illuminated with this light photo-electrons are emitted with a max kinetic energy of 0.75 eV. What would be the energy of the photons comprising the …

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Radiation

Q- Find the mean radiation power of an electron performing harmonic oscillations with amplitude a = 0.10 nm and frequency f = 6.5 X 1014 s-1

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Modern Physics: Mass energy relation

Q- The sun radiates electromagnetic energy at a constant rate of 3.92*1026 W.

(a) What is the change in the sun’s mass during each second due to radiating energy?

(b) The mass of the sum is 1.99*1030 kg. What fraction of the sun’s mass is lost during a human lifetime of 75 years?

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Modern Physics: Relativity

Q- A certain star is 18.6 light years away. How long would it take a space craft traveling at 0.950c to reach that star from earth as observed (a) on earth (b) on the spacecraft.

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Bohr Model

Q- In the Bohr model of the hydrogen atom, the speed of the electron is approximately 2.20 X 106 m/s. Find

(a) The force acting on the electron as it revolves in a circular orbit of radius 0.530 X 10-10 m and

(b) The centripetal acceleration of the electron.

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Momentum of a laser pulse

Q- A pulsed laser fires a 1000-MW pulse horizontally at a 10mg mass suspended vertically from a 4 cm long fiber of negligible mass. If the pulse lasts duration of 200 nanoseconds, and the radiation is completely absorbed by the mass, by what maximum angle is the pendulum deflected?

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Potential Well

Q- The longest wavelength line in the spectrum emitted by an electron trapped in an infinitely deep square well is 610 nm. What is the width of the well?

Solution:

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