Question

The value of Planck’s constant ‘h’ is:
$A.\text{ 6}\text{.63 x 1}{{\text{0}}^{-34}}\text{ Js}$
$B.\text{ 6}\text{.63 x 1}{{\text{0}}^{34}}\text{ Js}$
$C.\text{ 6}\text{.63 x 1}{{\text{0}}^{-23}}\text{ Js}$
$D.\text{ 6}\text{.63 x 1}{{\text{0}}^{34}}\text{ Js}$

Answer 1

Hint: Planck’s constant is a fundamental constant that is equal to the energy of electromagnetic radiation divided by its frequency. It was discovered by a German physicist Max Karl Ernst Ludwig Planck in 1900. His discovery paved the way for the quantum revolution and that constantly shows up all throughout quantum theory starting from de Broglie wavelength to Dirac’s equation.

Complete step-by-step solution:
In the late 1800s, physicists were working on a way to mathematically describe something called the black body spectrum above absolute zero where every molecule or atom in an object is wriggling around. As they wriggle, they emit radiation in the form of electromagnetic waves. Faster wriggles release shorter wavelengths and slower wriggles release longer wavelengths. A collection of particles will emit a mixture of wavelengths that is dependent on the temperature of the object. This is because the temperature is the measure of how quickly on an average the particles in an object is moving. At that time, they were using the equipartition theorem to figure out what sort of radiation should be coming out of an object at a given temperature. The idea was that particles wriggle in every way that it’s possible to wriggle and the energy is distributed amongst all of the wriggling variations. These wriggles were also called energy states and it worked well at low temperatures but as we approach temperatures above a few hundred degrees the theorem stopped working. It gave an answer that was infinitely too high.
Why did that happen? This was because the theorem assumed that there was no minimum energy state, the particles wriggles could always be a bit smaller. When they went to distribute the energy among all of the possible states too much energy ended up in those infinitely small wriggles. This was far off from what was measured, so they knew something was wrong but nobody knew why.
Then came Max Planck who figured out the solution in 1900. In a moment of frustration, he decided to see what would happen if instead of infinite states there was some minimum and all of the other energy states were just the multiple of this minimum and it worked which went on to be called the Planck’s law and was able to correctly predict the blackbody spectrum even at high temperatures and that minimum energy is now called the Planck’s constant. That little number that Planck came up with in his moment of desperation remains at the heart of all thing’s quantum. But not just quantum. By defining the shape of the blackbody spectrum, the Planck constant can be read in the color of the sun and the stars and the brightness of the different colors of the rainbow.
 So, how do we determine its value? It’s pretty simple, once we know Planck’s law and an object's temperature, we can calculate the Planck’s constant by just finding the brightest part of an object's heat glow which is $6.63 \times \text{ 1}{{\text{0}}^{-34}}\text{ Js}$ and represented by the symbol ‘h’.
So, the correct answer is option A.

Note: This value is determined experimentally and is out of the syllabus. So, it’s better to remember this little number which combined with a small handful of other fundamental constants governs the behavior of everything in this spacetime! This fundamental value is responsible for the quantization of energy levels ($E=h\nu $).