2. An electron is contained in a one-dimensional box of width 0.100 nm. Find the wavelengths of all photons that can be emitted by the electron in making transitions that would eventually get it from the n=4 state to the n=1 state.
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- 2. A particle of matter is moving with a kinetic energy of 6.55 eV. Its de Broglie wavelength is 1.34 x 10^-12 m. What is the mass of the particle? 4.68E-26 kg 1.40E-25 kg 1.99E-25 kg 1.17E-25 kg1. An electron initially moves in first excited state, if it absorb energy with frequency 5x10te Hz. Find the momentum of this electron before and after interaction with photon energy.51) A photon of energy 1.24 eV is absorbed by a molecule. a) What is its wavelength in cm and the reciprocal of its wavelength in cm-1? A..........cm B..........cm-1 The molecule transitions to an energy level of 0.24 eV, and emits a photon. b) What is the energy of the emitted photon (eV)? ..........eV c) What is its wavelength in cm and the reciprocal of its wavelength in cm-1? C..........cm D..........cm-1 d) Find D-B in cm-1. ..........cm-1 The second photon of energy 1.14 eV is absorbed by the same molecule. e) What is its wavelength in cm and the reciprocal of its wavelength in cm-1? E..........cm F..........cm-1 The molecule transitions to an energy level of 0.24 eV, and emits a photon. f) What is the energy of the emitted photon (eV)? ..........eV g) What is its wavelength in cm and the reciprocal of its wavelength in cm-1? G..........cm…
- 1. A free electron has the wavefunction p(x, t) = sin(kx – wt) and wave number k = 50nm-1 1.1 Determine the electron's de Broglie wavelength. 1.2 Determine the electron's momentum. 1.3 Determine the electron's kinetic energy. 2. An electron is trapped in an infinite potential well of width 1 cm. For what value of n will electron have an energy of 2 eV? 3. Give the Born interpretation of the wavefunction.4. An electron has a momentum py =1.30 x 10 kg.m/s. What is the minimum uncertainty in its position that will keep the relative uncertainty in its momentum (Apy/p) below 2.3%? (35.3 nm6. An electron in hydrogen atom is in initial state p(r, 0) = A(2µ100 + ¡Þ210 + 4Þ21–1 – 2i4211) where ynim are the eigenfunctions of the hydrogen atom a. Determine the constant A b. What is the probability of finding the electron in the first excited state? c. Write the state p(r, t) at time t, using energy eigenvalues as En = d. Find the expectation value of L in the state (r,t e. Find the expectation values of Lx and Ly in the state (r, t f. If measurement of L, led to the value -ħ what will be results of measurement of energy and the square of total orbital momentum immediately afterwards and what are their probabilities? hw n2
- An isolated atom of certain element emits light of wavelength 529 nm when the atom falls from its sixth excited state into its third excited state. The atom emits a photon of wavelength 422 nm when it drops from its seventh excited state into its third excited state. frind wavelength of the light radiated when the atom makes a transition from its seventh to its sixth excited state, in um. a. 21 b. 2.09 c. 2086.34 d 0.0209 e. 208. 634. In an electron microscope electrons are accelerated by a 1500-V potential drop to a velocity of approximately 1x108 m/s. a) Calculate the de Broglie wavelength of these electrons. b) What size objects should such a microscope be able to visualize? Explain your answer. c) If you desire a minimum uncertainty in the position of the electrons in your microscope of 1 Å, what is the maximum uncertainty that is acceptable in the momentum and velocity of the electrons?..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.
- Which of the following principal levels contains / (angular momentum quantum number) = 3? A. n = 2 level B. both n = 3 and n = 4 levels C. n = 3 level D. n = 4 level How many orbitals are contained in the n = 3 principal number of a given atom? What is the value of the angular momentum quantum number of a d orbital?5. An electron ( me = 9.11 × 10−31 kg ) and a bullet ( m = 0.02 kg) each have a velocity of magnitude 500 m/s, with a precision within 0.01%. In what limits is it possible to determine the position of objects along the velocity direction?What can you conclude from comparing your results for the electron and for thebullet?According to the Bohr model of the atom electrons exist in orbits around the atomic nucleus labelled by a quantum number n. The Bohr radius of an Hydrogen atom is 0.53 angstroms. What is the radius for the n = 3 orbit ? Select one: a. 1.59 angstroms. b. 4.77 angstroms. c. 3.18 angstroms. d. 0.176 angstroms. Clear my choice