Question

The energy of one mole of photons of radiation of frequency 2 \(\times\)10¹² H_z in Jmol^-1 is ________ (Nearest integer) 

[Given : \(h=6.626\times10^{-34}Js\)

 \(N_{A}=6.022\times10^{23}mol^{-1}\)]

Hint:

To calculate the energy of one mole of photons, first determine the energy of a single photon using E = hν. Then, multiply this by Avogadro’s number (NA) to find the energy for one mole.

Answer 1

Correct Answer: 798

To determine the energy of one mole of photons with a frequency of \(2 \times 10^{12} \, \text{Hz}\), use the formula for energy \(E\) of a photon:

\[ E = h \times \nu \]

where \(h\) is Planck's constant \((6.626 \times 10^{-34} \, \text{Js})\) and \(\nu\) is the frequency \((2 \times 10^{12} \, \text{Hz})\).

Substitute the given values into the equation:

\[ E = 6.626 \times 10^{-34} \, \text{Js} \times 2 \times 10^{12} \, \text{Hz} \]

Calculate:

\[ E = 1.3252 \times 10^{-21} \, \text{J per photon} \]

The energy for one mole of photons is found by multiplying the energy per photon by Avogadro's number \(N_A = 6.022 \times 10^{23} \, \text{mol}^{-1}\):

\[ E_{\text{mole}} = 1.3252 \times 10^{-21} \, \text{J/photon} \times 6.022 \times 10^{23} \, \text{photon/mol} \]

Perform the multiplication:

\[ E_{\text{mole}} = 797.52 \, \text{J/mol} \]

Rounding to the nearest integer, the energy is \(798 \, \text{J/mol}\).

Thus, the final energy of one mole of photons is 798 J/mol, which falls within the expected range of 798 to 798.