How much energy is contained in 1 mol of each of the
following?
1.X-ray photons with a wavelength of 0.135nm. Express the energy numerically in kilojoules per
mole.
2 .?-ray
photons with a wavelength of
2.75�10?5nm
.Express the energy
numerically in kilojoules per mole
Answer
Calculate the energy by using the following formula. E- c1) Here. E is energv, h is planck constant, c is velocity of the light, and lis wavelength of a radiation. Wavelength of the X – ray photons is 0.135 nm Covert the wavelegth into meters as shown below. 1 nm-10-9 m Thus, 0.135 nm- 0.135 x 10-9 m Now calculate the energy by substituting 6.626 10-34 J.s for h, 2.998x 108 m/s for c, and 0.135 x 10-9 m for 2 in the above formula(1 6.626 × 10-34J.s x 2.998x 108 m/s 0.135 x 10-9 m – 1.47 x 10-15J Calculate the energy per mole by multiplying the obtained energy with Avagadro’s number.
1.47 x 10-1J 6.023 x 1023 photons Photon mol – 8.85 x 108 J/mol – 8.85 x 105 kJ/mol Therefore, energy of the X -ray photons is 8.85 x 105 kJ/mol 2 wavelength of the γ-ray photons is 2.75 × 10-5 nm. 2.75 nm= 2.75 x 10-5 x 10-9 m=2.75 x 10-14 m Now calculate the energy by substituting 6.626 x 10-“J.s for h, 2.998×103 m/s for c, and 2.75 x 10-14 m for λ in the above formula(1) 6.626 x 10-4Js x 2.998 x 108 m/s 2.75 × 10-14 m 7.22 10-12 J Energy per mole is as follows: Thus, 7.22×10-12 J Photon – 4.35 x 1012 J/mol 6.023×1023 photons mol 4.35 x 109 kJ/mol Therefore, energy of the y-ray photons is 4.35 × 109 kJ/mol
