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 \[330J/g\] . (h=\[6.6 \times {10^{ - 34}}Jsec\] .)

Answer 1

Hint:Latent heat of fusion is the change in enthalpy of a substance when the substance melts. Photons are the elementary particles in quantum mechanics which possess dual character i.e. particle and wave character.

Complete answer:
The amount of heat required to change \[1g\] of a substance at the temperature of its melting point from the solid to the liquid state is referred to as the latent heat of fusion.
Max Plank discovered a mathematical relationship which is used to describe the intensities of light with various frequencies emitted by a hot solid at different temperatures. It was assumed that the atoms of the solid oscillate or vibrate with a definite frequency. A vibrating atom possess certain amount of energies \[E\] , which is expressed as
\[E = nh\nu \] , where \[h\] a constant called planck's constant with a value of $6.63 \times {10^{ - 34}}J\sec $ , \[\nu \] is the frequency of the photon and \[n\] is the number of photons (value of \[n\] is a whole number).
The number symbolized by n gives the quantum numbers of an atom. They represent the shell or the principal value of the quantum number.
In this case the frequency of the radiation is given as \[5 \times {10^{13}}{s^{ - 1}}\] . The latent heat of fusion is \[330J/g\] which is equal to the energy of photon emission of the atom. Inserting the values in the Plank’s equation,
\[Energy\; = nh\nu \]
\[330J/g = n \times 6.6 \times {10^{ - 34}}J\sec \times 5 \times {10^{13}}{s^{ - 1}}\]
$n = \dfrac{{330}}{{6.6 \times {{10}^{ - 34}} \times 5 \times {{10}^{13}}}}$
$n = 1 \times {10^{22}}$ .
Hence, the number of photons is $1 \times {10^{22}}$.

Note: Photons are considered as moving particles having zero mass and rest energy. They are neutral species that carry energy and momentum which is dependent on the frequency of oscillations. They travel with the speed of light when placed in empty space.