Modern Physics For Scientists And Engineers
2nd Edition
ISBN: 9781938787751
Author: Taylor, John R. (john Robert), Zafiratos, Chris D., Dubson, Michael Andrew
Publisher: University Science Books,
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Chapter 4, Problem 4.10P
To determine
(a)
The value of Planck's constant in
To determine
(b)
The frequency of
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Planck's radiation law can be written
ux
=
8лhc 1
25 eßhc/2-1
Show that the wavelength corresponding to the maximum energy density of the
radiation fulfills the condition
λmax T
=
.
constant
What is this constant? (This result is known as Wien's transition law.) Tip: you can
solve the constant approximation by e.g. iterating an equation of the form
Xn = 5 (1-e¯Xn-1)
with a suitable initial value x1.
In a photoelectric experiment it is found that a stopping potential of 1.00 V is needed to stop all the electrons when incident light of wavelength 225 nm is used and 1.5 V is needed for light of
wavelength 207 nm.
From these data determine Planck's constant. (Enter your answer, in eV s, to at least four significant figures.)
4.2367e-15 X ev s
From these data determine the work function (in eV) of the metal.
4.6
X ev
(b) Derive Rutherford scattering formula of alpha radiations from a gold foil on the basis of nuclear model of
atom. Why did planetary model of atom fail?
(c) What are the short comes in Rayleigh formula for the explanation of energy distribution in blackbody
radiations? Derive Planck's radiation formula from Rayleigh formula and express it in terms of wavelength.
Q#3 (a) Work function of the Aluminum is 4.08 eV.
I.
What is the threshold frequency required to produce photoelectrons from aluminum?
II.
Classify electromagnetic radiations that can produce photoelectrons.
III.
If light of frequency 4 x 1015 Hz is used to illuminate a piece of aluminum, then what is the maximum
energy and speed of emitted photoelectrons?
IV.
If the light described in part (ii) is increased by a factor of 2 in intensity, what would happen to the
maximum kinetic energy of photoelectrons?
f200 V What is the de
Chapter 4 Solutions
Modern Physics For Scientists And Engineers
Ch. 4 - Prob. 4.1PCh. 4 - Prob. 4.2PCh. 4 - Prob. 4.3PCh. 4 - Prob. 4.4PCh. 4 - Prob. 4.5PCh. 4 - Prob. 4.6PCh. 4 - Prob. 4.7PCh. 4 - Prob. 4.8PCh. 4 - Prob. 4.9PCh. 4 - Prob. 4.10P
Ch. 4 - Prob. 4.11PCh. 4 - Prob. 4.12PCh. 4 - Prob. 4.13PCh. 4 - Prob. 4.14PCh. 4 - Prob. 4.15PCh. 4 - Prob. 4.16PCh. 4 - Prob. 4.17PCh. 4 - Prob. 4.18PCh. 4 - Prob. 4.19PCh. 4 - Prob. 4.20PCh. 4 - Prob. 4.21PCh. 4 - Prob. 4.22PCh. 4 - Prob. 4.23PCh. 4 - Prob. 4.24PCh. 4 - Prob. 4.25PCh. 4 - Prob. 4.26PCh. 4 - Prob. 4.27PCh. 4 - Prob. 4.28PCh. 4 - Prob. 4.29PCh. 4 - Prob. 4.30PCh. 4 - Prob. 4.31PCh. 4 - Prob. 4.32PCh. 4 - Prob. 4.33P
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- The energy emitted by a black body's surface per unit area at a particul ar wavelength can be calcul ated using Planck's Radiation Law, which can be written as follows, 2nhc? E(2, T) = 25. (ehc/kT -1) where his Planck's constant 6.626 x 10-27 erg.s, c is the speed oflight, kis the Boltzmann constant = 1.38 x 10-18 erg/K, Tis the temperature in Kelvins and A is the wavelength in um. If E is given in erg/um?, what are the units of the constant 2n, given that the equation is valid and therefore dimensionally homogenous? If the speed of light is 3.00x10$ m/s, what value and unit should be used for c in this equation to maintain dimensional homogeneity? Note: erg is a unit of energy equal to 10-7 Joules and the whole expression (ehc/AkT – 1) ends up dimensionless. -arrow_forwardConsider a fission nuclear explosion producing a temperature of 24 million K (25∗107 K). a) What is be the peak wavelength of the thermally produced photons? b) What is the energy (in eV) for this peak wavelength photon?arrow_forward8πhy3 dv (a) Express the Planck radiation formula, Edv = c3 ehv/kT-1' terms of λ (and dλ), namely Edλ. (b) Solved=0 for λ = Amax in to determine the value of maxT in m-K, where max is the wavelength at which the blackbody spectrum has its maximum value at a given temperature T.arrow_forward
- Radiation has been detected from space that is characteristic of an ideal radiator at T = 2.728 K. (This radiation is a relic of the Big Bang at the beginning of the universe.) For this temperature, at what wavelength does the Planck distribution peak? In what part of the elec- tromagnetic spectrum is this wavelength?arrow_forward(a) A vacuum photocell is sequentially illuminated with light of different wavelengths 2. A voltmeter is used to determine that there is a different voltage between the cathode and the anode. V (iii) Determine a relation for Planck's constant in terms of pairs of voltage measurements at different wavelengths such that W₁ cancels out. (iv) Evaluate Planck's constant for the following pair of measurements: measurement 1 finds = 447 nm and V=635 mV, and measurement 2 finds = : 502 nm and V=339 mV.arrow_forward(Hand by writing ans.)A certain atom has an energy level of 3.50 eV above the ground state. When excited to this state, it remains 4.0µs, on average, before emitting a photon and returning to the ground state. i) What is the energy of the photon? What is the wavelength of the photon? ii) What is the smallest possible uncertainty in the energy of the photon?arrow_forward
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