EBK PHYSICS FOR SCIENTISTS & ENGINEERS
5th Edition
ISBN: 9780134296074
Author: GIANCOLI
Publisher: VST
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Chapter 38, Problem 6P
To determine
The minimum uncertainty in the energy of the state of an electron.
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(ii) A silicon detector contains a photoconductive layer of thickness 1 = 20mm. The refractive index of silicon is 4 and the absorption coefficient (a) of silicon in cm-1 is given by a = 10(7-6000) where I is wavelength in Å. Calculate the wavelength at which the quantum efficiency loss due to penetration through the device is equal to that due to re- flection at the surface.
(b) A photon is emitted by a doubly ionised lithium atom (Li²+) when an electron makes a
transition to the ground state. The wavelength of the photon is measured to be 10.83
nanometres.
Determine the principal quantum number and the energy of the initial state
The atomic number of lithium is Z = 3.
(2) In this experiment, why couldn't we observe the series of spectral lines that arise from electrons
falling to the ground state, nfinal = 1? This is the Lyman series, for which 22 (see eq. (16)) must be
replaced by 12 in both the numerator and denominator of the equation: 2 =-
1 n2
n =
R (n2-1)'
2,3,4,5, ..
Chapter 38 Solutions
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- (a) The Lyman series in hydrogen is the transition from energy levels n = 2, 3, 4, ... to the ground state n = 1. The energy levels are given by 13.60 eV En n- (i) What is the second longest wavelength in nm of the Lyman series? (ii) What is the series limit of the Lyman series? [1 eV = 1.602 x 1019 J, h = 6.626 × 10-34 J.s, c = 3 × 10° m.s] %3D Two emission lines have wavelengts A and + A2, respectively, where AA <<2. Show that the angular separation A0 in a grating spectrometer is given aproximately by (b) A0 = V(d/m)-2 where d is the grating constant and m is the order at which the lines are observed.arrow_forward2) The energy levels of a quantum-mechanical, one-dimensional, anharmonic oscillator maybe approximated as 2 =(n * (n + )' En hw ;n = 0,1,2,... (++) = The parameter x, usually « 1, represents the degree of anharmonicity. Show that, to the first order in x and the fourth order in u (= ħw/kgT), the specific heat of a system of N such oscillators is given by C = Nk [(1-u² + *)+ 4x (: + *)]. 240 80 Note that the correction term here increases with temperature.arrow_forward(a) If the position of a chlorine ion in a membrane is measured to an accuracy of 1.00 µm , what is its minimum uncertainty in velocity, given its mass is 5.86×10-26 kg ? (b) If the ion has this velocity, what is its kinetic energy in eV, and how does this compare with typical molecular binding energies?arrow_forward
- The speed of an electron is known to be between 3.0 x 106 m/s and 3.2 x 106 m/s. Estimate the smallest possible uncertainty in its position.arrow_forward7) A particular laser oscillating at the resonant wavelength of 1 um has a M value of 1010. The photon number in the cavity at the threshold pumping rate is (Write the Answer as an integral number without using exponents)arrow_forwardEstimate the uncertainty in the position of a 50 kg person moving at 2m/sec?arrow_forward
- (i) Using Bohr model for atomic hydrogen, obtain energy levels for the 2s, 3s and 3p states in theactual number with the unit of [eV]. We consider a transition that electron in the 3p state emitsa photon and make a transition to the 2s state. What is the frequency ν of this photon ?(ii) Now we do not include electron spin angular momentum, and just estimate an effect of amagnetic field B on this transition (Normal Zeeman effect) with orbital angular momentum.How many lines of optical transition do we expect ? What is the interval of the frequency in thefield B = 0.1 Tesla ?(iii) In this situation, we do not expect transition from 3s to 2s state if the electron is initially in the3s state, Explain the reason.(iv) We now consider an effect of magnetic field B to a free electron spin (not in Hydrogen, but afree electron). The magnetic field of B = 1.0 Tesla will split the energy level into two (Zeeman)levels. Obtain the level difference in the unit of [eV] from the value of magnetic…arrow_forward(i) Using Bohr model for atomic hydrogen, obtain energy levels for the 2s, 3s and 3p states in theactual number with the unit of [eV]. We consider a transition that electron in the 3p state emitsa photon and make a transition to the 2s state. What is the frequency ν of this photon ?(ii) Now we do not include electron spin angular momentum, and just estimate an effect of amagnetic field B on this transition (Normal Zeeman effect) with orbital angular momentum.How many lines of optical transition do we expect ? What is the interval of the frequency in thefield B = 0.1 Tesla ? Only solve (ii) pleasearrow_forward(i) Using Bohr model for atomic hydrogen, obtain energy levels for the 2s, 3s and 3p states in theactual number with the unit of [eV]. We consider a transition that electron in the 3p state emitsa photon and make a transition to the 2s state. What is the frequency ν of this photon ?(ii) Now we do not include electron spin angular momentum, and just estimate an effect of amagnetic field B on this transition (Normal Zeeman effect) with orbital angular momentum.How many lines of optical transition do we expect ? What is the interval of the frequency in thefield B = 0.1 Tesla ?(iii) In this situation, we do not expect transition from 3s to 2s state if the electron is initially in the3s state, Explain the reason. Solve (iii) only pleasearrow_forward
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