3. In the Bohr model of the hydrogen atom, what is the de Broglie wavelength for the electron when it is in (a) n = 1 level and (b) n = 4 level? In each case, compare the de Broglie wavelength to the circumference 2Trn of the orbit.
Atomic Spectra
According to the Bohr model of an atom, the electron in an atom moves around a nucleus in fixed orbits with specific energies known as energy levels. The orbital energies are quantized. The electrons remain in these energy levels until they emit or absorb a photon of a particular wavelength, the quantum of energy. If the electron emits a photon, it then falls back to a lower energy level, and if it absorbs a photon, the electron rises to higher energy levels. The photons released or absorbed in these transitions of an electron are studied and analyzed on a screen as atomic spectra.
Ruby Lasers
Lasers are devices that emit light using atoms or molecules at a certain wavelength and amplify the light to produce a narrow beam of radiation. It works as per the principle of electromagnetic radiation. Their source of emission contains the same frequency and same phase. It was invented in the year 1960 by the great noble scientist, Theodore Maiman.
Balmer Series
The spectrum of frequency observed when electromagnetic radiation is emitted from an atom when it goes from higher energy state to lower state, is known as emission spectrum. This transition occurs when an excited electron moves from higher to lower state. It has many possible electron transitions and each transition has a specific energy difference.
Emission Spectrum
Every state of matter tries to be at minimum potential energy or it can be said that the atoms of element/ substance arrange themselves such that overall energy is minimum.
![1. In an experiment to study the photoelectric effect, a scientist measures the kinetic energy
of ejected electrons as a function of the frequency of radiation hitting a metal surface. She
obtains the following plot. The point labelled "vo" corresponds to light with a wavelength of
680 nm.
Frequency
a. What is the value of vo in s-1?
b. What is the value of the work function of the metal in J?
c. What happens when the metal is irradiated with light of frequency less than vo?
d. Note that when the frequency of the light is greater than vo, the plot shows a
straight line with a nonzero slope. Why is this the case?
e. Can you determine the slope of the line segment discussed in part (d)? Explain.
2. An electron starting from rest, accelerates through a potential difference of 418 V. What
is the final de Broglie wavelength of the electron, assuming that its final speed is much
less than the speed of light?
3. In the Bohr model of the hydrogen atom, what is the de Broglie wavelength for the electron
when it is in (a) n = 1 level and (b) n = 4 level? In each case, compare the de Broglie
wavelength to the circumference 2Tr, of the orbit.
4. A scientist has devised a new method of isolating individual particles. He claims that this
method enables him to detect simultaneously the position of a particle along an axis with
a standard deviation of 0.12 nm and its momentum along this axis with a standard
deviation of 3.0 x1025 kg-m/s. Use the Heisenberg uncertainty principle to evaluate the
validity of this claim.
5. The Schrödinger equation for a particle of mass m that is constrained to move freely along
a line between 0 and a is
(8n²mE`
W(x) = 0
dx2
with the boundary condition
y(0) = p(a) = 0
In this equation, E is the energy of the particle and (x) is its wave function. Solve this
differential equation for (x), and apply the boundary conditions.
Electron
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