Exercise 7.46 with feedback You may want to reference (DA pages 296 306) section

Question

Exercise 7.46 with feedback You may want to reference (DA pages 296 306) section 7.2 while completing this problem. How much energy is contained in 1 mol of each of the following? Part A X-ray photons with a wavelength of 0.135 nm Express the energy numerically in kilojoules per mole. Eh 1.4724 10 18 Submit My Answers Give U Incorrect; Try Again; 5 attempts remaining Part B r-ray photons with a wavelength of 2.58x10 5 nm. Express the energy numerically in kilojoules per mole. 7.7046511627907 10 15 Submit My Answers Give U kJ/mol kJ/mol

Explanation / Answer

Solution :-

Part A given data

Wavelength of x-ray photon = 0.135 nm

Energy E= ? kJ/mol

Formula to calculate the energy using the wavelength is as follows

Energy (E) = h*c / l

Where , h = planks constant (6.626E-34 J.s) , c= speed of light (3.0E8 m/s) and l = wavelength in meter

Now lets convert given wavelength from nm to meter

0.135 nm * 1 m / 1E9 nm = 1.35E-10 m

Now lets put the values in the formula and calculate the energy per photon

E= h*c/ l

E = (6.626E-34 J.s * 3.0E8 m/s )/ 1.35E-10 m

E = 1.47E-15 J

Now lets convert this energy from per photon to per mol photon

1.47E-15 J * 6.022E23 photon / 1 photon = 8.86E8 J/ mol

Now lets convert J to kJ

8.85E8 J per mol * 1 kJ / 1000 J = 8.86E5 kJ/mol

Therefore energy per mole of photon for X- ray = 8.86*105 kJ/mol

Part B

Given data

Gamma ray photon wavelength = 2.58E-5 nm

Energy (E)= ?

Lets convert wavelength from nm to meter

2.58E-5 nm * 1 m / 1E9 nm = 2.58E-14 m

Formula to calculate the energy using the wavelength is as follows

Energy (E) = h*c / l

Where , h = planks constant (6.626E-34 J.s) , c= speed of light (3.0E8 m/s) and l = wavelength in meter

Now lets put the values in the formula and calculate the energy per photon

E= h*c/ l

E = (6.626E-34 J.s * 3.0E8 m/s )/ 2.58E-14 m

E = 7.70 E-12 J per photon

Now lets convert this energy from per photon to per mol photon

7.70E-12 J * 6.022E23 photon / 1 photon = 4.64E12 J/ mol

Now lets convert J to kJ

4.64E12 J per mol * 1 kJ / 1000 J = 4.64E9 kJ/mol

Therefore energy per mole of photon for gamma ray = 4.64*109 kJ/mol

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