Question

Find the number of photons of radiation of frequency $5 \times {10^{13}}{s^{ - 1}}$ that must be absorbed in order to melt one gm ice when the latent heat of fusion of ice is $330{\text{ J}}$ . $\left( {h = {\text{ }}6.6{\text{ }} \times {\text{ }}{{10}^{34}}{\text{ J sec}}} \right)$

Answer 1

From the latent heat of fusion of ice, determine the energy needed to melt one gram of ice. Then use the equation $E = n \times h \times \nu$ to calculate the number of photons of energy needed.

Complete Step by step answer: In this question, you are given the latent heat of fusion of ice and the frequency of electromagnetic radiation. You are also given the value of the Planck's constant. You are supposed to calculate the number of photons of the electromagnetic radiation.
The latent heat of fusion of ice is $330{\text{ J/g}}$ . When one gram of ice melts, the energy required is $330{\text{ J}}$ .
Suppose n photons are needed
Write the expression for the energy of n photons as follows:
$E = n \times h \times \nu$ … …(1)
Here, E is the energy, n is the number of photons, h is the Planck’s constant and $\nu$ is the frequency.
The value of the planck’s constant $h = {\text{ }}6.6{\text{ }} \times {\text{ }}{10^{34}}{\text{ J sec}}$ . Th value of the frequency of the radiation is $5 \times {10^{13}}{s^{ - 1}}$
The energy of the radiation is $330{\text{ J}}$ .
Substitute the values in the equation (1) to calculate the number of photons.
$E = n \times h \times \nu$
$\Rightarrow 330{\text{ J}} = n \times 6.6{\text{ }} \times {\text{ }}{10^{34}}{\text{ J sec}} \times 5 \times {10^{13}}{s^{ - 1}}$
$\Rightarrow n = \dfrac{{330{\text{ J}}}}{{6.6{\text{ }} \times {\text{ }}{{10}^{34}}{\text{ J sec}} \times 5 \times {{10}^{13}}{s^{ - 1}}}}$
$\Rightarrow n = 1{\text{ }} \times {\text{ }}{10^{22}}{\text{ photons}}$
Hence, the number of photons of radiation of frequency $5 \times {10^{13}}{s^{ - 1}}$ that must be absorbed in order to melt one gm ice is $1{\text{ }} \times {\text{ }}{10^{22}}$ .

Note: An electromagnetic radiation has energy associated with it. An electromagnetic radiation has several photons associated with it. From the frequency or wavelength of the electromagnetic radiation, it is possible to calculate the energy of a single photon. It is also possible to calculate the energy of one mole of photons.