1) An electron, m= 9.109 x 10-31 kg, is moving in a two dimensional box. The frequency of the n =1 to n = 2 transition is 6 x 10¹2/sec. A) What is the length of the box? B) What wavelength of light is emitted if the electron transits from n = 4 to n=2?
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=1 to n = 2 transition is 6 x 10¹2/sec.
A) What is the length of the box?
B) What wavelength of light is emitted if the electron transits from n = 4 to n=2?
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- Hydrogen Like Atoms Part A: Find the frequency of light f radiated by an electron moving from orbit n1=2 to n2=1 inside of a He+ ion. Part B: In the Bohr model of hydrogen, the radius of the nth orbit is defined as r_n= a0n^2/Z, where a0= 4πϵℏ^2/m_ee^2= 5.29×10−11m is called the Bohr radius. Find the radius r1 of a valence orbital for a He+ ion.Photons of a certain infrared light have an energy of 1.70x10 J. (a) What is the frequency of this IR light? Hz (b) Use A = c/f to calculate its wavelength in nanomneters. nmc) 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.
- 19. A certain atom holds an electron with an initial energy of 6.4 eV above the ground state energy. At some time later the energy is 3.2 eV above ground state. What is the frequency associated with the emission of the photon for this transition? A. 9.4x10¹4 Hz B. 7.7x10¹4 Hz C. 2.1x10¹4 Hz D. 8.9x1014 HzIf the wavelength of an electron is 4.58 ✕ 10−7 m, how fast is it moving? km/s(b) If the electron has a speed equal to 3.80 ✕ 106 m/s, what is its wavelength? mDetermine the distance between the electron and proton in an atom if the potential energy U of the electron is 10.1 eV (electronvolt, 1 eV = 1.6 × 10-19 J). Give your answer in Angstrom (1 A = 10-10 m). Answer: Choose... +
- Determine the distance between the electron and proton in an atom if the potential energy ?U of the electron is 16 eV (electronvolt, 1 eV =1.6×10−19=1.6×10−19 J). Give your answer in Angstrom (1 A = 10-10 m).2. A photon has a frequency of 7.50 x 1014 Hz, a. Determine the energy and the momentum of this photon. b. If all the energy of this photon were to be converted to mass, determine the equivalent mass for the particle. c. A microscopic specimen has a wavelength of 8.2 x 10-14m and a speed of 1.1 x 10° m/s. Determine the mass of this microscopic specimen.A hydrogen atom emits a photon that has momentum 6.977 × 10-27 kg·m/s. This photon is emitted because the electron in the atom falls from a higher energy level into the n = 1 level. What is the quantum number of the level from which the electron falls? Use values of h = 6.626 × 10-34 J·s, c = 2.998 × 108 m/s, and e = 1.602 × 10-19 C.