The Bohr model for the hydrogen atom posits that the atom's electron can only occupy circular orbits, with the circumference of each orbit containing an integral number of de Broglie wavelengths. Suppose that an electron in a particular hydrogen atom is in the first excited orbit, corresponding to n = 2. (a) What is the radius (in nm) of this electron's orbit around the atom's nucleus (a proton)? nm (b) What is the de Broglie wavelength (in nm) for an electron in this orbit? nm

The Bohr model for the hydrogen atom posits that the atom's electron can only occupy circular orbits, with the circumference of each orbit containing an integral number of de Broglie wavelengths. Suppose that an electron in a particular hydrogen atom is in the first excited orbit, corresponding to n = 2. (a) What is the radius (in nm) of this electron's orbit around the atom's nucleus (a proton)? nm (b) What is the de Broglie wavelength (in nm) for an electron in this orbit? nm

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter5: Matter Waves

Section: Chapter Questions

Problem 24P

See similar textbooks

Similar questions

When a hydrogen atom is in its ground state, what are the shortest and longest wavelengths of the photons it can absorb without being ionized?
An atom (not a hydrogen atom) absorbs a photon whose associated wavelength is 375 nm and then immediately emits a photon whose associated wavelength is 580 nm. How much net energy is absorbed by the atom in this process?
An electron has a de Broglie wavelength equal to the diameter of a hydrogen atom in its ground state. (a) What is the kinetic energy of the electron? (The Bohr radius is 0.0529 nm.) eV(b) How does this energy compare with the magnitude of the ground-state energy of the hydrogen atom? many orders of magnitude smallerabout 10 times as small about the sameabout 10 times as largemany orders of magnitude larger
For the thermal radiation from an ideal blackbody radiator with a surface temperature of 2000 K, let Ic represent the intensity per unit wavelength according to the classical expression for the spectral radiancy and IP represent the corresponding intensity per unit wavelength according to the Planck expression.What is the ratio Ic/IP for a wavelength of (a) 400 nm (at the blue end of the visible spectrum) and (b) 200 mm (in the far infrared)? (c) Does the classical expression agree with the Planck expression in the shorter wavelength range or the longer wavelength range?
thanks. The work function of sodium is 2.3 eV. What is the longest wavelength that can cause photoelectric emission? What should be the stopping potential if the sodium atom is illuminated by light of λ = 400 nm?
Calculate the De-Broglie wavelength for, A biological virus of size d is 10 nm – 300 nm, mass m is 10 ^ -15 kg and average speed v = 1 mm/s. An atomic electron size of d is 2.8 fm, mass m is 9.1 x 10^-31 kg, and in orbital speed in first Bohr orbit is v= 2.6 x 10^6 m/s
If a photon of wavelength 0.0665 nm hits a free electron and is scattered at an angle of 35◦ from its original direction, findat. the change in wavelength of this photon,b. the wavelength of the scattered photon,vs. the change in energy of the photon (is it a loss or a gain?), and d. the energy gained by the electron.
Calculate the velocities of electrons with de Broglie wavelengths of 1.7×103 nm and 5.0 nm, respectively.
Through what minimum potential difference must an electron in an x-ray tube be accelerated so that it can produce x rays with a wavelength of 0.100 nm?
In a photoelectric effect experiment, electrons emerge from a copper surface with a maximum kinetic energy of 1.10 eV when light shines on the surface. The work function of copper is 4.65 eV. Which one of the following values is closest to the wavelength of the light? (h = 6.626 × 10-34 J ∙ s, c = 3.00 × 108 m/s, 1 eV = 1.60 × 10-19 J) Group of answer choices 220 nm 1100 nm 150 nm 360 nm
An electron of momentum p is at a distance r from a stationary proton. The electron has kinetic energy K = p2/2me . The atom has potential energy UE = -kee2/r and total energy E = K + UE. If the electron is bound to the proton to form a hydrogen atom, its average position is at the proton but the uncertainty in its position is approximately equal to the radius r of its orbit. The electron’s average vector momentum is zero, but its average squared momentum is approximately equal to the squared uncertainty in its momentum as given by the uncertainty principle. Treating the atom as a one-dimensional system, (a) estimate the uncertainty in the electron’s momentum in terms of r. Estimate the electron’s (b) kinetic energy and (c) total energy in terms of r. The actual value of r is the one that minimizes the total energy, resulting in a stable atom. Find (d) that value of r and (e) the resulting total energy. (f) State how your answers compare with the predictions of the Bohr theory.
What are (a) the energy of a photon corresponding to wavelength 1.00 nm, (b) the kinetic energy of an electron with de Broglie wavelength 1.00 nm, (c) the energy of a photon corresponding to wavelength 1.00 fm, and (d) the kinetic energy of an electron with de Broglie wavelength 1.00 fm?