Question

Carbon absorbs energy at a wavelength of 150. nm. The total amount of energy emitted by a carbon sample is J. Calculate the number of carbon atoms present in the sample, assuming that each atom emits one photon.

Answer 1

The given question is incomplete. The complete question is as follows.

Carbon absorbs energy at a wavelength of 150 nm. The total amount of energy emitted by a carbon sample is $1.93 \times 10^{5} J$. Calculate the number of carbon atoms present in the sample, assuming that each atom emits one photon.

Explanation:

It is given that the energy at which C-atom absorbs energy is 150 nm. So, energy emitted by the carbon atom will have same wavelength at which C-atom absorbs the energy.

As we know that relation between energy and wavelength is as follows.

                  E = $\frac{hc}{\lambda}$

where,  h = Planck's constant = $6.624 \times 10^{-34} J sec$

             c = speed of light = $3 \times 10^{8} m/s$

             $\lambda$ = 150 nm = $150 \times 10^{-9}$

Therefore, energy of one carbon atom is calculated as follows.

                E = $\frac{hc}{\lambda}$

                  = $\frac{6.624 \times 10^{-34} Js \times 3 \times 10^{8} m/s}{150 \times 10^{-9}}$

                 = $1.324 \times 10^{-18} J$

As the total energy emitted by the carbon sample is  $1.93 \times 10^{5} J$. Let us assume that the number of C-atoms in the sample be x and it is calculated as follows.

           $E_{total} = n \times E_{1C-atom}$

                     n = $\frac{E_{total}}{E_{1C-atom}}$

                        = $\frac{1.93 \times 10^{5}}{1.324 \times 10^{-18} J}$

                        = $1.45 \times 10^{23}$

Thus, we can conclude that number of carbon atoms present in the sample, are $1.45 \times 10^{23}$.