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Chapter 3: Problem 14

The ratio of the energies of two different radiations whose frequencies are \(3 \times 10^{14} \mathrm{HZ}\) and \(5 \times 10^{14}\) \(\mathrm{HZ}\) is _______.

Short Answer

Expert verified
Answer: The ratio of the energies of the two radiations is 0.6.

Step by step solution

01

Write down the given frequencies and Planck's constant

The given frequencies are: \(\nu_1 = 3 \times 10^{14}\) Hz \(\nu_2 = 5 \times 10^{14}\) Hz Planck's constant is: \(h = 6.63 \times 10^{-34}\) Js
02

Calculate the energies of the radiations

Using the formula for the energy of a photon, we can calculate the energies of both radiations: \(E_1 = h\nu_1 = (6.63 \times 10^{-34} \text{ Js})(3 \times 10^{14} \text{ Hz}) = 1.989 \times 10^{-19} \text{ J}\) \(E_2 = h\nu_2 = (6.63 \times 10^{-34} \text{ Js})(5 \times 10^{14} \text{ Hz}) = 3.315 \times 10^{-19} \text{ J}\)
03

Calculate the ratio of the energies

Now, we can find the ratio of the energies by dividing the energy of the first radiation by the energy of the second radiation: \(\frac{E_1}{E_2} = \frac{1.989 \times 10^{-19} \text{ J}}{3.315 \times 10^{-19} \text{ J}} = 0.6\) The ratio of the energies of the two radiations is 0.6.

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