(a) If an electron makes a transition from the n = 7 Bohr orbit to the n = 3 orbit, determine the wavelength of the photon created in the process. nm (b) Assuming that the atom was initially at rest, determine the recoil speed of the hydrogen atom when this photon is emitted. m/s

-27 (a) What is the wavelength (in nm) of a photon that has a momentum of 4.50 x 10 kg · m/s? nm (b) Find its energy in eV. eV

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.

See attached.

9. Considering the photoelectric effect; a) If a material has a cutoff wavelength of 780 nm what is the work function of the material? b) What is the maximum speed of liberated electrons when light with a wavelength of 410 nm is used to illuminate the material? If a liberated electron has 3.2349 eV of kinetic energy and it was a photon emitted from a hydrogen atom transition that liberated it, what energy level transition occurred? State both the initial and final energy level.

A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.

A x-ray having wavelength 0.077nm strikes a free and ‘stationary’ electron. This causes the electron to recoil and an x-ray having longer wavelength to be emitted at angle θ to the direction of the incident x-ray. If the electron recoils with kinetic energy 0.9238 eV, determine the angle at which the second x-ray emerges