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17 Nov 2019

Charged particles in the external field

(a) Calculate the wavelength and kinetic energy of an electron in a beam of electrons accelerated by a voltage increment by 135 V.

(b) What is the wavelength of a proton with a kinetic energy of 135 eV? Compare it to the wavelength of an electron with the same energy.

(c) At what distance does an alpha particle (a nucleus of He) pass a gold atomic nucleus, if it experiences a force of 3.8 N?

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Reid WolffLv2

28 Jan 2019

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Just as light waves have particle behavior, a moving particle has a wave nature. The faster the particle is moving, the higher its kinetic energy and the shorter its wavelength. The wavelength, Î», of a particle of mass m, and moving at velocity v, is given by the de Broglie relation

Î»=hmv

where h=6.626Ã10â34 Jâ s is Planck's constant.

This formula applies to all objects, regardless of size, but the de Broglie wavelength of macro objects is miniscule compared to their size, so we cannot observe their wave properties. In contrast, the wave properties of subatomic particles can be seen in such experiments as diffraction of electrons by a metal crystal.

Part A

The mass of an electron is 9.11Ã10â31 kg. If the de Broglie wavelength for an electron in a hydrogen atom is 3.31Ã10â10 m, how fast is the electron moving relative to the speed of light? The speed of light is 3.00Ã108 m/s.

Express your answer numerically as a percent.

Part B

The mass of a golf ball is 45.9 g . If it leaves the tee with a speed of 60.0 m/s , what is its corresponding wavelength?

CHEM 1430 LIGHT LAB SPRING 2018 A Danish physicist, Neils Bohr, a post-doctoral student in J. J. Thomson's lab and friend of Rutherford, took up the problem of electron arrangement within the atom. Bohr's breakthrough was recognizing Balmer's fixed emission wavelengths, when taken with Planck's Relationship, led to the conclusion the shells, like the radiation emitted, must be quantized (have set, specific energles). Bohr proposed the electrons circulated about the madeus, much like planets cirde surãin seres of concentric shells of increasing size. Each shell stood at a fixed (set) distance from the nucleus with the shell nearest the nucleus taking the m and a shell further away taking the n in the B-R equation. The integral values of m and n taken with the discrete wavelength led Bohr to propose the shells were "quantized," meaning electrons could only exist at the surface of the shells. When an electron moved from a high shell, n, to a low shell, m, light of a foxed wavelength was emitted Bohr reasoned the shells were special due to this quantized nature. An electron in a shell occupied what Bohr described as a "steady state," meaning the electron could circulate about the nucleus without loss or gain of energy. This steady state proposition, which conflicted with classical physics, could not be explained by then available data but was required for Bohr's proposed structure to be stable. Later work revealed the wave-particle duality of the electron which lead to acceptance of the Steady State Proposition. The energy of an electron in any shell, represented by n, can be calculated using an equation derived from combining the Balmer-Rydberg and Planck equations. The energy of an electron in the no shell is given by é¦¯.h RL where hcR,-2.18x10-*) where Ru, is the Rydberg's Constant for the hydrogen atom, h is Planck's Constant and c is the speed of light NOTE: The energy is given a nexative value to refect the stabillting, attractive force between the negatively charged electron and the positively charged nucleus. As the shell number n increases, the attractive force decreases leading to a rising shell energies (E, increases, values less negative). ACTIVITY Calculate the energles for an electron in the first 7 shells of the hydrogen atom using the above relationship, recording the values in the center column of the Hydrogen the right-hand column in the table, convert the shell with the exponent of 10 Improper sclentific notation is typically used to plot data covering several orders of magnitude (powers of ten). Shell Energy Table. For energies to improper scientific notation Hydrogen Shell Energy Table Shell Value, n Calculated Shell Energy.ã Express Shell Energy in improper Scientific Notation, x 10-1 Page 9 of 12

Nuclear Decay Equations

Learning Goal:

To predict the products of alpha emission, beta emission, positron emission, and electron capture.

Radioactivity is the spontaneous emission of radiation from an unstable nucleus. There are five major types of radioactive decay:

Alpha (Î±) radiation consists of helium nuclei. The helium nucleus is a small particle containing two protons and two neutrons (42He).

Beta (Î²) radiation consists of electrons. In nuclear equations, the standard format for representing a beta particle using superscripts and subscripts is 0â1e.

Positron emission results from the conversion of a proton in the nucleus to a neutron. The ejected positron is a particle that has the same mass as an electron but an opposite charge. In nuclear equations, the standard format for representing a positron using superscripts and subscripts is 01e .

Electron capture is the capture of an inner shell electron by a proton in the nucleus. The process emits gamma (Î³) radiation and results in a proton converting to a neutron. Gamma radiation consists of high-energy electromagnetic radiation.

Gamma (Î³) radiation consists of high-energy radiation, and contains no particles and thus they have no mass. In nuclear equations, the standard format for representing gamma radiation using superscripts and subscripts is 00Î³.

Balancing a decay equation

There are two main rules to remember when balancing nuclear equations:

The total of the superscripts in the reactants and products must be the same.

The total of the subscripts in the reactants and products must be the same.

For an isotope of an element, the superscripts are mass numbers, and the subcripts are atomic numbers:

Mass number â¶ AAtomic number â¶ Z X âµ Chemical symbol

Where the mass number (A) is the sum of the number of proton and number of neutrons in the nucleus, atomic number (Z) is the number of protons in the nucleus, and chemical symbol (X) is the symbol of the specific element.

Part A

Identify the nuclide produced when americium-241 decays by alpha emission:

241 95Amâ42He + ?

Express your answer as an isotope using prescripts.

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Part B

Identify the nuclide produced when phosphorus-32 decays by beta emission:

3215Pâ 0â1e + ?

Express your answer as an isotope using prescripts.

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Part C

Identify the nuclide produced when fluorine-18 decays by positron emission: