2.3. Find the de Broglie wavelength of (a) an electron, and (b) a proton with speeds of 5 × 106 m/s and compare with the radius of the hydrogen atom, ao. Would either of these particles behave like a wave inside the H atom?
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- a. Conceptually, discuss the particle-wave duality of light. Discuss the implications of this in combination with the de Broglie (pronounced “de Broy”) equation. b. The electron of a hydrogen atom is usually no further than 1.0 Å from the proton. We can therefore say the upper limit of the radius of an isolated hydrogen atom is roughly 1.0 Å. How does the de Broglie wavelength of the electron compare to this radius? (The velocity of an electron in the first principal energy level is about 2.2 x 106 m/s). Explain why wave-particle duality is so important for quantum mechanics, yet not required in macroscopic systems that are well described by classical mechanics. c. Comment as to whether neutrons with velocity 4.14 x 103 m/s may be used to determine structures of molecules in a diffraction-based experiment. You may consider the relevant distance between atoms in molecules to be on the order of 1 Å.Calculate the de Broglie wavelength for : a. a jogger of mass 77 kg runs with at speed of 4.1 m s1. b. an electron of mass 9.11x10-31 kg moving at 3.25x105 m s1 (Given the Planck's constant, h =6.63x1034J s)la) The maximum value of the Planck spectrum for 91 photons at 6 Kelvin is (k=Boltzmann constant) Select one: O a. 182.00 Ob. 16.92k Oc. 546.00 O d. zero Oe. 91.00 b) A box contains 3 identical fermions. What is the partition function if each particle can occupy any of 10 single- particle states? Assume that the energy for each of these states is zero. Select one: O a. 1 Ob. 495.00 Oc. 100 Od. zero Oe. infinity
- 2.1. Find the de Broglie wavelength of the following particles: (i) an electron in a semiconductor having average thermal velocity at T = 300 K and an effective mass of me = amo, where a is a constant, (ii) a helium atom having thermal energy at T = 300 K, (iii) an a-particle (He4 nucleus) of kinetic energy 10 MeV.The root mean square speed of the hydrogen molecules at temperature t °C is given by 3x8.31 x (t+273) m 2 x 10-3 Calculate the de Broglie wavelength (in nanometers) of the hydrogen molecules at temperature 24 °C. The mass of the hydrogen molecule is 2 x 1.66 x 10-27 kg. Use two decimals in your answer.Determine the maximum wavelength of thephoton that hydrogen in the excited stateni = 6 can absorb. The energy of the groundstate of hydrogen is −13.6 eV, the speed oflight is 2.99792 × 108 m/s and Planck’s constant is 6.62607 × 10−34 J · s.Answer in units of nm. What would be the next smaller wavelengththat would work?Answer in units of nm.
- A) What is the approximate wavelength emitted from helium represented by the bright yellow emission line below? What is it's frequency in HZ and energy in eV? (1 eV= 1.6 x 10-19 joules). B) If the excited helium electron that emits a yellow photon in this line starts with a potential energy of 8 eV, what is the potential energy of the electron afterwards? Assume that the emission of a yellow photon is allowed by the laws of quantum mechanics. Also don't worry about the other electron.4. In Section 1.3 we used dimensional analysis to show that the size of a hydrogen atom can be understood by assuming that the electron in the atom is wave-like and non-relativistic. In this problem we show that, if we assume the electron in the atom is a classical electron described by the theory of relativity, dimensional analysis gives an atomic size which is four orders of magnitude too small. Consider a relativistic, classical theory of an electron moving in the Coulomb potential of a proton. Such a theory only involves three physical constants: m, /4mc9, and e, the maximum velocity in relativity. Show that it is possible to construct a length from these three physical constants, but show that it too small to characterize the size of the atom.| 1+ 19. An electron (mass m) with initial velocity i = voi + voj is in an electric field É = -E,k. If 1o is initial de-Broglie wavelength of electron, its de-Broglie wavelength at time t is given by do a. A = 1+ m2 t? b. A= 1+ t2 m²u λο c. A = 1+ t2 2m² v do d. A = 2+
- 3.1. What is the de Broglie wavelength of an electron that has been accelerated through a potential difference of AV = 150 V?A) Calculate the de Broglie wavelength of a neutron (mn = 1.67493×10-27 kg) moving at one six hundredth of the speed of light (c/600). Enter at least 4 significant figures. (I got the answer 949.4 pm but it is wrong, please help) B) Calculate the velocity of an electron (me = 9.10939×10-31 kg) having a de Broglie wavelength of 230.1 pm.An electron is confined to a rigid box that is 1.20nm long. If the electron is in the third excited state what is the de broglie wavelength? What are all of the possible wavelengths of light that the electron can emit as it goes to ground state?
