The problems given be low are due next week, but your group should work on them

Question

The problems given be low are due next week, but your group should work on them today. Taking the average wavelength of visible light to be 3.50 times 10^2 nm, answer the following questions: a) What is the average frequency of this light expressed in s^-1? a) What is the wavenumber in cm^-1? c) What is the energy, in J, of single photon having this wavelength? A coffee cup containing 165 mL of water is placed in a microwave oven: How many microwave photons having a wavelength of 1.31 times 10^8 nm are needed to raise the temperature of the water from 25.0 degree C to 95.0 degree C? Recall that the heat capacity of water is 4.184 J/gm degree C. The density of water may be table as 1.00 g/cm^3.

Explanation / Answer

a.) = 350 nm = 350x10-9m = 350x10-7 cm

c = 3x108 m/s

c=

= c/ = 3x108/350x10-9 cm = 8.57x1014 /s

= 8.57x1014 /s

b.) Wavenumber = 1/

= 1/350x10-7 cm = 2.84x104 /cm

c) E = h = hc/

h = 6.625x10-34 Js

c = 3x108 ms-1

= 6.625x10-34 Js x 3x108 ms-1 /350x10-9m = 5.6x10-19J

E = 5.6x10-19J (energy of each photon)

3. mass of water, m = 165 mL = 165g (d= 1g/cc)

s = 4.184 J/g ° C

t = t2-t1 = 95 ° C- 25 ° C= 70 ° C

Q = mst

= 165g x 4.184 J/g C x 70 ° C = 48325J

E = nhc/ (n is the number of photons)

= 1.31x108nm = 0.13m

h = 6.625x10-34 Js

c = 3x108 ms-1

n = E/hc = 48325 J x 0.13 m / 6.625x10-34 Js x 3x108 ms-1 =3.16x1028 Photons

n = 3.16x1028 Photons

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