Question

What is an example of a Planck’s constant practice problem?

Answer 1

Planck suggested a quantum theory of radiation that marks the atoms and molecules as bundles of energy called as quantum or a photon. The energy of a quantum of radiation is directly proportional to the frequency of radiation. The formula on this basis is $E=h\nu$. h is Planck’s constant that has a value $6.626\times {{10}^{-34}}J.s$.

Complete answer:
Planck’s quantum theory of radiation explained the particle nature of electromagnetic radiation. According to this theory, atoms and molecules emit energy in a discontinuous pattern in the form of bundles called quantum or photons. The energy of the photons is directly proportional to the frequency of radiation that gave rise to the formula $E=h\nu$, where E is the energy in Joules, h is Planck’s constant, and $\nu$is the frequency of radiation calculated in hertz.
Now, example of a Planck’s constant practice problem is:
A red light consists of photons that emit the energy of$2.84\times {{10}^{-19}}J$. Calculate their frequency?
As we know, $E=h\nu$, where E is given as, h (Planck’s constant) is $6.626\times {{10}^{-34}}J.s$, and frequency$\nu$is unknown. So, solving for $\nu$, rearranging the equation we have,
$\nu =\dfrac{E}{h}$
$\nu =\dfrac{2.84\times {{10}^{-19}}J}{6.626\times {{10}^{-34}}J.s}$
$\nu =\dfrac{4.29\times {{10}^{14}}}{s}$= $4.29\times {{10}^{14}}Hz$.
Hence, the Planck’s practice problem is explained on the basis of $E=h\nu$.

Note:
The unit of hertz is the reciprocal of seconds as $1Hz=\dfrac{1}{s}$ , therefore the frequency is calculated in hertz as Planck’s constant involves the unit in joule second. Planck's quantum theory became a basis for the photoelectric effect as it involves the ejection of photons. The equation $E=h\nu$ can be written with the number of photons N as $E=Nh\nu$.