Energy and the Hydrogen Atom 8. The radiation used in a microwave oven has a wav

Question

Energy and the Hydrogen Atom 8. The radiation used in a microwave oven has a wavelength of 11.5 cm a. How many photons are required to heat 0.264 qt of coffee from 21.0°C to 65.0°C Assume the specific heat and density of coffee are the same as water b. If the power of the microwave oven is 1,20o w aW 1 J/s), and its efficiency is 91.0%, how long would it take to heat the coffee in part a above? 9. Which orbital in each of the following pairs is higher in energy? Explain. (a) 3s or 3p in a hydrogen atom (b) 3s or 3p in a helium atom (c) 4s or 3p in a hydrogen atom (d) 4s or 3p in a helium atom (e 4s or 3d in a hydrogen atom (f) 4s or 3d in a helium atom 9-139

Explanation / Answer

8.

a) volume of coffee = 0.264 qt

let's convert this ml since water density = 1.00 g/ml (1 L = 1.057qt and 1L = 1000ml)

So, 0.264 qt x (1L/1.057 qt) x (1000ml/1L) = 249.76 ml 249.76 ml x (1.00g/ml) = 249.76 g

we know that, q = m*c*delta T where q is heat energy, m is mass, c is specific heat and delta T is change in temperature.

delta T = 65.0 - 21.0 = 44.0 0C

specific heat, c = 4.184 J/(g * 0C)

q = 249.76 g x 4.184 J/(g * 0C) x 44.0 0C

q = 45979.82 J

wavelength of photon = 11.5 cm = 0.115 m

we know that,

E = hc/lambda

E=6.626*10-34 * 3x108 / 0.115 m

E= 1.72 x 10-24

hence now,

Now all you have to do is figure out how many photons of microwave radiation are needed to get a total energy of

45979.82 J

= 45979.82 / (1.72x10-24)

~ ~ answer = 2.7 x 1028 photons

b) given power = 1200W

energy = 45979.82 J *100/91                 ( efficiency = 91%)

             =50527.27

as power = energy / time

~ time = energy / power

~time= 50527.27 / 1200

~ time= 42 sec

9.

a) 3p has higher energy because This electron correlation introduces the effect of electron-electron repulsion. That in turn generates an energy splitting of the orbitals with the same n but different l.

b) 4s has higher energy since n+l for both 3s and 4p are same. Look for the subshell with large value of principle quantum no, that is n=4(4s). hence 4s has more energy.

c) 4s has higher energy because it is filled first according to aufbau principle thus having more energy.

d) 3d has higher energy According to the Aufbau principle, the 4s sublevel is filled before the 3d sublevel because the 4s is lower in energy

e) 3d has higher energy.

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