Cesium was discovered in natural mineral waters in 1860 by...

Cesium was discovered in natural mineral waters in 1860 by R. W. Bunsen and G. R. Kirchhoff using the spectroscope they invented in $1859 .$ The name came from the Latin caesius ( ${ }^{u}$ sky blue") because of the prominent blue line observed for this element at $455.5 \mathrm{~nm}$. Calculate the frequency and energy of a photon of this light.

Cesium was discovered in natural mineral waters in 1860 by
R. W. Bunsen and G. R. Kirchhoff using the spectroscope they invented in $1859 .$ The name came from the Latin caesius ( ${ }^{u}$ sky blue") because of the prominent blue line observed for this element at $455.5 \mathrm{~nm}$. Calculate the frequency and energy of a photon of this light.

Key Concepts

Photon

A photon is a fundamental particle of light that exhibits both wave-like and particle-like properties. Photons are the elementary quanta of electromagnetic radiation and are characterized by their energy, which is directly proportional to their frequency.

Wavelength and Frequency Relationship

In electromagnetic waves, the speed of light is constant and is equal to the product of the wave's frequency and wavelength. This relationship allows one to calculate the frequency of light when its wavelength is known, highlighting the inverse relationship between wavelength and frequency.

Planck's Constant and Photon Energy

Planck's constant is a key fundamental constant in quantum mechanics that establishes the proportionality between the energy of a photon and its frequency through the equation E = h?. This concept is crucial in understanding quantum phenomena and the quantization of electromagnetic energy.

Transcript

00:01 Okay, so in this problem we are asked to find the energy and the frequency of a photon given its wavelengths.

00:09 So the equation that we're going to use is the following.

00:13 E, which stands for the energy of the photon, equals h, which is a constant called planck constants, times the frequency.

00:23 And we also know that the frequency can be written as c, which is the speed of light over the wavelength of the photon.

00:32 So we're going to use both equations here.

00:35 Now let's remember that the h value, or planck's constant, is 6 .626 times 10 to the negative 34.

00:47 And the units are joules per times seconds.

00:53 So that's going to be the value that we're going to use for h.

00:57 We do not know the frequency or the energy, but we do know that the speed of light is another constant that's known as 2 .9979 times 10 to the 8 meters per second.

01:15 And we are given the wavelength in the problem.

01:18 The wavelength is 445 .5 nanometers, which we can convert to meters so that we have consistency in the units.

01:28 So we're going to say that it's 445 .5 times 10 to the negative 9 meters.

01:39 So we're going to use this equation, since we have all of the values, to calculate the energy.

01:45 So the energy is going to be equals to h times c over the wavelength.

01:51 We're going to use all the values that we have...

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