How many times longer is the wavelength of electromagnetic radiation used in a microwave oven at 2.45 GHz than the copper K-$\alpha$ 1 X-ray radiation used in X-ray diffraction studies with an energy of 1.29 $\times$ 10^-15 J?

Question

Quizplus · Accepted Answer

The wavelength of electromagnetic radiation can be determined using the formula: lambda = c/f, where c is the speed of light (approx. 3 x 10^8 m/s) and f is the frequency in hertz. 
For the microwave oven with f = 2.45 GHz,
lambda = c/f = (3 x 10^8 m/s)/(2.45 x 10^9 Hz) = 0.122 m
For the X-ray radiation with energy of 1.29 x 10^10 J,
lambda = h*c/E = (6.63 x 10^-34 J*s * 3 x 10^8 m/s)/(1.29 x 10^10 J) = 1.38 x 10^-11 m
The ratio of these wavelengths is:
0.122 m / 1.38 x 10^-11 m = 7.91 x 10^9
Therefore, the wavelength of the microwave radiation is 7.92 x 10^9 times longer than the X-ray radiation used in X-ray diffraction studies. The closest answer choice is (C).

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