To calculate the frequency (\(f\)) of sodium based on its wavelength (\(A\)), use the equation:
\[ f = \frac{c}{A} \]
where:
- \(c\) is the speed of light (\(3.00 \times 10^8 , \text{m/s}\))
- \(A\) is the wavelength in meters.
Assuming you have the wavelength for sodium from your data table, substitute that value into the equation to calculate the frequency.
Example Calculation: Let's say the wavelength you determined for sodium is \(A = 589 , \text{nm}\) (which is a common wavelength in the sodium D-line). First, convert it to meters: \[ A = 589 , \text{nm} = 589 \times 10^{-9} , \text{m} \]
Now, calculate the frequency:
\[ f = \frac{c}{A} = \frac{3.00 \times 10^8 , \text{m/s}}{589 \times 10^{-9} , \text{m}} \]
\[ f \approx 5.08 \times 10^{14} , \text{Hz} \]
Now that you have calculated the frequency, you can find the energy (\(E\)) using the equation:
\[ E = h \times f \]
where:
- \(h\) is Planck’s constant (\(6.63 \times 10^{-34} , \text{J.s}\))
- \(f\) is the frequency calculated earlier.
Using the frequency from above:
\[ E = (6.63 \times 10^{-34} , \text{J.s}) \times (5.08 \times 10^{14} , \text{Hz}) \]
\[ E \approx 3.37 \times 10^{-19} , \text{J} \]
Assuming the above wavelength, the approximate energy of the sodium photon is \(3.37 \times 10^{-19} , \text{J}\).
Make sure to plug in the specific wavelength from your data table for the accurate calculation.
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