The velocity of electron in the first Bohr orbit of radius 0.5 A.U. is 2.24 × 10 m/s. Calculate the period of revolution of the electron in the same orbit.
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- In the early 1900s the normal Zeeman effect was useful to determine the electron’s e/m if Planck’s constant was assumed known. Calcium is an element that exhibits the normal Zeeman effect. The difference between adjacent components of the spectral lines is observed to be 0.0168 nm for = λ 422.7 nm when calcium is placed in a magnetic fi eld of 2.00 T. From these data calculate the value of eh/m and compare with the accepted value today. Calculate e/m using this experimental result along with the known value of h.In Millikan's oil-drop experiment, one looks at a small oil drop held motionless between two plates. Take the voltage between the plates to be 2241 V and the plate separation to be 2 cm. The oil drop (of density 0.81 g/cm3) has a diameter of 4.0 ×10-6 m. Find the charge on the drop, in terms of electron units.What is the radius of the electron orbit in a singly ionized helium ion?
- So Determine the distance between the electron and proton in an atom if the potential energy ?U of the electron is 15.4 eV (electronvolt, 1 eV =1.6×10−19=1.6×10−19 J). Give your answer in Angstrom (1 A = 10-10 m)If the radius of a calcium ion is 0.22 nm, how much energy does it take to singly ionize it? Give your answer in electron-volts (eV) with precision 0.1 eV. Give your answer to 2 significant digits.Compute the oscillation frequency of the electron and the expected absorption or emission wavelength in a Thomson- model hydrogen atom. Use R = 0.053 nm.
- Ex. 20: Find the value of energy of electron in eV in the third Bohr orbit of hydrogen atom. (Rydberg's constant (R) = 1.097 × 107 m¹, Planck's constant (h) = 6.63 × 10-34 J-s, velocity of light in air (c) = 3 × 108 m/s).In an avalanche , one electron ,starting at the cathode , multiplies to 1000 over a distance of 10 mm , the ionization :coefficient (a) is 0.56 ionizations /mm 0.69 ionizations/mm 0.2 ionizations/mm O 0.33 ionizations/mm O The number of ionizing collisions on average made by an electron per unit drift : in the direction of the field is called Statistical time lag O Townsends first ionization collision coefficient Townsends second ionization collision coefficient Attachment coefficientThe deflector plates of a Thomson appliance are 6.0 cm long and separated by 1.2 cm. The distance between the front edge of the plate and the tube is 30.0 cm. The energy assigned to the electrons of the beam is 2.8 keV (can make an illustration for a good understanding) (a) If the potential of 25 V is applied to the deflector plates, what will be the deviation of the beam on the screen? (b) Find the module of the crossed magnetic field that would allow the beam to pass through the plates, without suffering any deviation. Answer a) 7.36 mm b) 6.64 x 10^ - 5 T
- t was observed that the atoms of a substance had so much energy that it separated the electrons and protons of the atom. What is most likely the state of matter of the substance?In Thomson’s e/m experiment, does it matter whether the electron passing through interacts fi rst with the electric fi eld or with the magnetic fi eld or both simultaneously? Explain.c) The Bohr model of the atom postulated electrons orbiting around the nucleus in stable orbits. De Broglie explained what orbits could exist by postulating that electrons (and any- thing else) with momentum p have an associated wavelength λ, given by λ=h/p where h is Planck's constant. i) For an electron orbiting around a proton (the Bohr model), equating the centripetal force with the Coulomb force gives the expression v² = e²/(4πεmer). Calculate the speed of an electron orbiting at the Bohr radius, ˜Â = 0.053 nm. ii) Calculate the momenta and the de Broglie wavelengths of the electron of part (i) and of a bird (a racing pigeon) that weighs 0.350 kg and flies at 100 km per hour. iii) Compare the wavelength for the electron that you obtain in (ii) with the circumference of the orbit. Comment on this comparison. Explain briefly what it implies about the other possible orbits of the Bohr model and how the higher orbits might be predicted.