Fundamentals Of Physics - Volume 1 Only
11th Edition
ISBN: 9781119306856
Author: Halliday
Publisher: WILEY
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Chapter 39, Problem 53P
To determine
To find:
Verification of Eq.39-39,
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The light observed that is emitted by a hydrogen atom is explained by a simple model of its structure with one proton in its nucleus and an electron bound to it, but only with internal energies of the atom satisfying
EH=−RH/n2EH=−RH/n2
where RHRH is the Rydberg constant and nn is an integer such as 1, 2, 3 ... and so on. When a hydrogen atom in an excited state emits light, the photon carries away energy and the atom goes into a lower energy state.
Be careful about units. The Rydberg constant in eV is
13.605693009 eV
That would be multiplied by the charge on the electron 1.602× 10-19 C to give
2.18× 10-18 J
A photon with this energy would have a frequency f such that E=hf. Its wavelength would be λ = c/f = hc/E. Sometimes it is handy to measure the Rydberg constant in units of 1/length for this reason. You may see it given as 109737 cm-1 if you search the web, so be aware that's not joules.
The following questions are intended to help you understand the connection between…
In the quantum mechanical treatment of the hydrogen atom, which one of the following combinations of quantum numbers is not allowed?
a) n=3, l=0, ml=0
b) n=3, l=1, ml= -1
c) n=3, l=2, ml= 2
d) n=3, l=2, ml= -1
e) n=3, l=3, ml=2
A collection of atoms has 20% of the sample in a state 7.60 eV above the ground state. If these emit coherent radiation, what is the wavelength of the laser light produced in nanometers? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) Give your answer as a whole number.
Chapter 39 Solutions
Fundamentals Of Physics - Volume 1 Only
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- An electron in a hydrogen atom makes a transition from the n=1 state to the n=3 state (1eV= 1.6 x10^-19 J and h = 6.63 x 10^-34 J s= 4.136 x 10^-15 Ev/hz c =3.0 x10^8 m/s) what is the energy of the photon absorbed in transition and what is the frequency of the absorbed photon energy?arrow_forwardKα X-ray lines are emitted from a target with atomic number Z when an electron jumps down from n = 2 to n = 1 state. If I use the approximate formula for the electron energy levels En = -(Z-1)2(13.6)/n2 eV, I can derive Moseley’s law √f = a(Z−b). What are the values of the constants a and b? A) a = 4.96*107 Hz1/2, b = 0 B) a = 4.96*107 Hz1/2, b = 1 C) a = 1.24*1017 Hz1/2, b = 1 D) a = 1.24*1017 Hz1/2, b = 0 E) none of these.arrow_forwardA hydrogen atom is excited from its ground state to the state with n= 4. (a) How much energy must be absorbed by the atom? Consider the photon energies that can be emitted by the atom as it de-excites to the ground state in the several possible ways. (b) How many different energies are possible; what are the (c) highest, (d) second highest, (e) third highest, (f) lowest, (g) second lowest, and (h) third lowest energies?arrow_forward
- The longest wavelength line of the Balmer Series for hydrogen occurs at 656.3 nm corresponding to the transition from n2 = 3 to n1 = 2. Determine the value for the Rydberg constant for hydrogen using these values.arrow_forwardwhat is the shortest wavelength of light that can be emitted by a hydrogen atom with initial configuration of 7d^1?arrow_forwardWhat is the probability of the electron in the 1s state of the hydrogen atom being at a radius greater than the Bohr radius a0?arrow_forward
- Assume that in the Stern–Gerlach experiment as described forneutral silver atoms, the magnetic field B has a magnitude of 0.50 T.(a) What is the energy difference between the magnetic moment orientationsof the silver atoms in the two subbeams? (b) What is thefrequency of the radiation that would induce a transition betweenthese two states? (c) What is the wavelength of this radiation, and (d)to what part of the electromagnetic spectrum does it belong?arrow_forwardFor the hydrogen atom in its ground state, calculate (a) the probability density c2(r) and (b) the radial probability density P(r) for r = a, where a is the Bohr radius.arrow_forwardFind the shortest wavelength of a photon that can be emitted by a hydrogen atom, for which the initial state is n = 12.arrow_forward
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