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Solved: If you put 120 volts of electricity through a
Chapter , Problem 6.82(choose chapter or problem)
If you put 120 volts of electricity through a pickle, the pickle will smoke and start glowing orange- yellow. The light is emitted because sodium ions in the pickle become excited; their return to the ground state results in light emission. (a) The wavelength of this emitted light is 589 nm. Calculate its frequency. (b) What is the energy of 0.10 mol of these photons? (c) Calculate the energy gap between the excited and ground states for the sodium ion. (d) If you soaked the pickle for a long time in a different salt solution, such as strontium chloride, would you still observe 589-nm light emission?
Questions & Answers
QUESTION:
If you put 120 volts of electricity through a pickle, the pickle will smoke and start glowing orange- yellow. The light is emitted because sodium ions in the pickle become excited; their return to the ground state results in light emission. (a) The wavelength of this emitted light is 589 nm. Calculate its frequency. (b) What is the energy of 0.10 mol of these photons? (c) Calculate the energy gap between the excited and ground states for the sodium ion. (d) If you soaked the pickle for a long time in a different salt solution, such as strontium chloride, would you still observe 589-nm light emission?
ANSWER:Step 1 of 4
(a) Here we have to calculate the frequency.
The wavelength of this emitted light is \(589 \mathrm{~nm}=5.89 \times 10^{-7} \mathrm{~m}\)
It is known that frequency \(v=\frac{c}{\lambda}\), where \(\mathrm{c}\) is the velocity of light \(=3 \times 10^{8} \mathrm{~m} / \mathrm{s}\) and \(\lambda\) is the wavelength.
Now substituting the values, frequency can be calculated as,
\(\begin{aligned}v =\frac{c}{\lambda} \\=\frac{3 \times 10^{8} \mathrm{~m} / \mathrm{s}}{5.89 \times 10^{-7} \mathrm{~m}} \\=5.09 \times 10^{14} \mathrm{~s}^{-1}\end{aligned}\)
Thus the frequency is found to be \(5.09 \times 10^{14} \mathrm{~s}^{-1}\).