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Chapter 2: Problem 40

An FM radio station broadcasts at 99.5 MHz. Calculate the wavelength of the corresponding radio waves.

Short Answer

Expert verified
The wavelength of the radio waves broadcast by the FM radio station at 99.5 MHz is approximately 3.015 meters.

Step by step solution

01

Convert frequency to hertz

The frequency is given as 99.5 MHz. To convert this to Hz, we'll multiply by 1,000,000 (since 1 MHz = 1,000,000 Hz). \(99.5 MHz × 1,000,000 Hz/MHz = 99,500,000 Hz\)
02

Calculate the wavelength

Now that we have the frequency in Hz, we can use the wavelength equation mentioned earlier: Wavelength (λ) = Speed of light (c) / frequency (f) Fill in the values: \(λ = \frac{3.0 × 10^8 m/s}{99,500,000 Hz}\)
03

Solve for the wavelength

Divide the speed of light by the frequency: \(λ = \frac{3.0 × 10^8 m/s}{99,500,000 Hz} = \frac{3.0 × 10^8 m/s}{9.95 × 10^7 Hz}\) \(λ = 3.015 \times 10^{7/9} m/s = 3.015 m\) The wavelength of the radio waves broadcast by the FM radio station at 99.5 MHz is approximately 3.015 meters.

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Most popular questions from this chapter

Write equations corresponding to the following: a. the fourth ionization energy of Se b. the electron affinity of \(S^{-}\) c. the electron affinity of \(\mathrm{Fe}^{3+}\) d. the ionization energy of \(\mathrm{Mg}\)

One of the emission spectral lines for \(\mathrm{Be}^{3+}\) has a wavelength of \(253.4 \mathrm{nm}\) for an electronic transition that begins in the state with \(n=5 .\) What is the principal quantum number of the lower-energy state corresponding to this emission? (Hint: The Bohr model can be applied to one- electron ions. Don't forget the \(Z\) factor: \(Z=\) nuclear charge \(=\) atomic number.

In each of the following sets, which atom or ion has the smallest radius? a. \(\mathrm{H}, \mathrm{He}\) b. \(\mathrm{Cl}, \mathrm{In}, \mathrm{Se}\) c. element \(120,\) element \(119,\) element 116 d. \(\mathrm{Nb}, \mathrm{Zn}, \mathrm{Si}\) e. \(\mathrm{Na}^{-}, \mathrm{Na}, \mathrm{Na}^{+}\)

The ionization energy for a \(1 s\) electron in a silver atom is \(2.462 \times 10^{6} \mathrm{kJ} / \mathrm{mol}\) a. Determine an approximate value for \(Z_{\text {eff }}\) for the Ag \(1 s\) electron. Assume the Bohr model applies to the 1 s electron. \(Z_{\mathrm{eff}}\) is the apparent nuclear charge experienced by the electrons. b. How does \(Z_{\text {eff }}\) from part a compare to \(Z\) for Ag? Rationalize the relative numbers.

In the second row of the periodic table, \(\mathrm{Be}, \mathrm{N},\) and \(\mathrm{Ne}\) all have positive (unfavorable) electron affinities, whereas the other second-row elements have negative (favorable) electron affinities. Rationalize why Be, \(N,\) and Ne have unfavorable electron affinities.
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