Yellow light emitted from a sodium lamp has a wavelength (lambda) of 580nm. Calculate the frequency of the yellow light.

Understand the Problem

The question is asking to calculate the frequency of yellow light emitted from a sodium lamp, given its wavelength of 580 nm. We will use the formula that relates wavelength and frequency, which is c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency.

Answer

$5.17 \times 10^{14} \text{ Hz}$

Steps to Solve

Identify the variables

From the problem, we know:

The speed of light, $c = 3 \times 10^8 \text{ m/s}$
The wavelength, $\lambda = 580 \text{ nm}$. We need to convert this to meters, knowing that $1 \text{ nm} = 1 \times 10^{-9} \text{ m}$.

So, $$ \lambda = 580 \text{ nm} = 580 \times 10^{-9} \text{ m} $$

Rearrange the formula to find frequency

The formula connecting wavelength and frequency is given by: $$ c = \lambda \nu $$ We rearrange this to find the frequency ($\nu$): $$ \nu = \frac{c}{\lambda} $$

Substitute the known values into the equation

Now we can substitute the values of $c$ and $\lambda$ into the formula: $$ \nu = \frac{3 \times 10^8 \text{ m/s}}{580 \times 10^{-9} \text{ m}} $$

Calculate the frequency

Perform the division: $$ \nu = \frac{3 \times 10^8}{580 \times 10^{-9}} \approx 5.17 \times 10^{14} \text{ Hz} $$

The frequency of yellow light emitted from a sodium lamp is approximately $5.17 \times 10^{14} \text{ Hz}$.

More Information

This frequency falls within the visible spectrum, which is why we can see yellow light from the sodium lamp. The speed of light is a constant, which plays a crucial role in linking frequency and wavelength.

Tips

A common mistake is forgetting to convert the wavelength from nanometers to meters. This is essential for the units to match when using the equation ( c = \lambda \nu ).

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