Question

Concept:

Engergy & momentum of light?

Uncertainty Principle?

Answer 1

Light as a Particle

Light is a wave, but that's not all it is. Light acting like a wave was relatively easy to produce. Even in the middle of the 19th century we knew that light could reflect, refract, and diffract. And, as far as we could tell, those effects could only be explained by light being a wave. But then, Albert Einstein noticed something. He showed in his photoelectric effect experiment that light could also behave as a particle.

In that experiment, he shone light onto some metal and found that electrons were ejected. When the light was brighter, more electrons were ejected, but those electrons didn't move any faster - they didn't have any extra energy. However, if he increased the energy of the light, making the light bluer, the electrons did move faster. Suffice it to say, this was not what he expected, and these observations led him to the realization that light must behave both as a wave and a particle; this is called wave-particle duality.

Energy of a Photon

It turns out that light contains energy in discrete packets (or particles) called photons. The amount of energy in those photons is calculated by this equation, E = hf, where E is the energy of the photon in Joules; h is Planck's constant, which is always 6.63 * 10^-34 Joule seconds; and f is the frequency of the light in hertz.

The electrons in the metal were being hit by these photons, which gave them the energy needed to escape. Bluer light has more energy because it has a higher frequency, so the electrons that escaped were moving faster. Brighter light contained more photons, so more electrons left the metal, but those electrons were no faster than with the dimmer light because they could only be hit by one photon of light at a time.

This idea of electrons colliding with photons of light is why these observations can only be explained by treating light as a particle, rather than a wave. A wave can't collide with anything, so if light was purely a wave, then brighter light should lead to higher energy electrons.

Momentum of a Photon

If light contains particles called photons, perhaps they should have momentum like any other particle. In fact, light is both a wave and a particle. So, not only does it have a momentum, it also has a wavelength. We relate these two quantities using something called the de Broglie wavelength: p = h / lambda. This equation says that the momentum of a photon, p, measured in kilogram meters per second, is equal to Planck's constant, h, divided by the de Broglie wavelength of the light, lambda, measured in meters.

UNCERTAINITY PRINCIPLE:

according to Uncertainity principle if one knows the precise momentum of the particle, it is impossible to know the precise position, and vice versa. This relationship also applies to energy and time, in that one cannot measure the precise energy of a system in a finite amount of time. Uncertainties in the products of “conjugate pairs” (momentum/position) and (energy/time) were defined by Heisenberg as having a minimum value corresponding to Planck’s constant divided by 4π. More clearly:

ΔpΔx≥h/4π

ΔtΔE≥h/4π

Where Δ refers to the uncertainty in that variable and h is Planck's constant

The uncertainty principle says that we cannot measure the position (x) and the momentum (p) of a particle with absolute precision. The more accurately we know one of these values, the less accurately we know the other. Multiplying together the errors in the measurements of these values (the errors are represented by the triangle symbol in front of each property, the Greek letter "delta") has to give a number greater than or equal to half of a constant called "h-bar". This is equal to Planck's constant (usually written as h) divided by 2π. Planck's constant is an important number in quantum theory, a way to measure the granularity of the world at its smallest scales and it has the value 6.626 x 10-34 joule seconds.

One way to think about the uncertainty principle is as an extension of how we see and measure things in the everyday world. You can read these words because particles of light, photons, have bounced off the screen or paper and reached your eyes. Each photon on that path carries with it some information about the surface it has bounced from, at the speed of light. Seeing a subatomic particle, such as an electron, is not so simple. You might similarly bounce a photon off it and then hope to detect that photon with an instrument. But chances are that the photon will impart some momentum to the electron as it hits it and change the path of the particle you are trying to measure. Or else, given that quantum particles often move so fast, the electron may no longer be in the place it was when the photon originally bounced off it. Either way, your observation of either position or momentum will be inaccurate and, more important, the act of observation affects the particle being observed.

The uncertainty principle is at the heart of many things that we observe but cannot explain using classical (non-quantum) physics. Take atoms, for example, where negatively-charged electrons orbit a positively-charged nucleus. By classical logic, we might expect the two opposite charges to attract each other, leading everything to collapse into a ball of particles. The uncertainty principle explains why this doesn't happen: if an electron got too close to the nucleus, then its position in space would be precisely known and, therefore, the error in measuring its position would be minuscule. This means that the error in measuring its momentum (and, by inference, its velocity) would be enormous. In that case, the electron could be moving fast enough to fly out of the atom altogether.