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Marina CMI [18]
3 years ago
15

Carbon absorbs energy at a wavelength of 150. nm. The total amount of energy emitted by a carbon sample is J. Calculate the numb

er of carbon atoms present in the sample, assuming that each atom emits one photon.
Biology
1 answer:
aivan3 [116]3 years ago
7 0

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}.

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