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Electromagnetic radiation behaves both as particles (called photons) and as waves. Wavelength (Î») and frequency (Î½) are related according to the equation

c=Î»ÃÎ½

where c is the speed of light (3.00Ã108 m/s). The energy (E in joules) contained in one quantum of electromagnetic radiation is described by the equation

E=hÃÎ½

where h is Planck's constant (6.626Ã10â34 Jâ s). Note that frequency has units of inverse seconds (sâ1), which are more commonly expressed as hertz (Hz).

Part A

A microwave oven operates at 3.00 GHz . What is the wavelength of the radiation produced by this appliance?

Express the wavelength numerically in nanometers.

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Related questions

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?

LIGHT LAB SPRING 2018 CHEM 1430 Ill. Quantization of Electromagnetic Radiation In 1894, the German physidist, Max Plank, was working for a utility company to maximize visible light output from incandescent lamps using minimum power. Based on theoretical considerations, Planck postulated that electromagnetic energy could only be emitted at discrete values, rather than the continuum of predicted by classical physics, as multiples of the frequency of the radiation. Planck's Postulate took the mathematical form: EÂ·hv where the energy emitted, in Joules, is the product of a constant, h, known as Planck's Constant, and the frequency of the radiation, v. Planck's Postulate was experimentally verified and h found to have the value of 6.626 x 1034 Js(Joule seconds). The idea that electromagnetic radiation energy had specific frequency dependent energy was termed a "quantum of action," a distressing finding for the dlassically trained Planck. Despite his objections, Planck adopted this quantization of energy as a last resort to reconcile experiment with theory. This discovery set the stage for the early understanding of atomic structure, led to the term "photon" to describe the packet of energy carried by light waves, led to an understanding of the photoelectric effect, eventually leading to the development of general quantum theory Planck's Relationship, in combination with the tight equation, c the energy of a photon from frequency or wavelength. Î» w, allow expressions to be written to calculate ACTIVITY 4: QUANTIZATION OF THE ENERGY OF RADIATION To practice cakculations with Planck's Relationship, complete the following table, showing work with units in the right mest column, Convert given frequency to energy or given wavelength to energy. Take the value for Planck's Constant, h, to be 6.626 x 10"Js, show a calculation string include dimensions, reporting the final value to the proper number of significant figures Spectral Region Wavelength Frequency Energy in J/photon Show Calculation String Î» in meters v in s or cps X-ray 6.0 x 10"m Blue light 4.5 x 10m Infrared 4.1 x 10" cps Microwave 7.3 x 101 cps Radio Wave 3.0x 10 m IV. Bohr's Quantum Model for the Hydrogen Atom Ernest Rutherford's Gold Foil Experiment of 1911 demonstrated the nuclear structure of the atom. Questions remained as to how electrons were arranged in the atom. The most common belief called for the negatively charged the late 19h century recognized a particle (an electron) traveling around a body (the positively charged nucleus) would continuously radiate energy, slowing over time, eventually falling into the nucleus. Matter would collapse. Page 8 of 12

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