Question

Looking at the spectral lines from the hydrogenspectrum of light, pictured below, and give theWavelength (m), Frequency (Hz), Velocity (m/s),Energy (J) for line c. Use scientific notation asneeded and 3 significant figures ex. 1.23E5.

Answer 1

ANSWER and EXPLANATION

We want to identify the parameters of the line in the electromagnetic spectrum.

The wavelength of line c is given as 486.13 nanometers. Converting this to meters, we have that the wavelength of line c is:

`\begin{gathered} \lambda=486.13*10^(-9) \\ \lambda=4.86E-7\text{ }m \end{gathered}`

To find the frequency of line c, apply the relationship between the velocity of light and wavelength:

`f=(c)/(\lambda)`

where c = velocity of light in a vacuum

f = frequency of the light

Hence, the frequency of line c is:

`\begin{gathered} f=(3.00*10^8)/(4.85*10^(-7)) \\ f=6.19E14\text{ }Hz \end{gathered}`

The velocity of light in a vacuum is given by:

`c=3.00E8\text{ }m\/s`

The energy of the line can be found using the formula:

`E=hf`

where E = energy

h = Planck's constant = 6.63E-34 Js

Hence, the energy of line c is:

`\begin{gathered} E=6.63*10^(-34)*6.19*10^(14) \\ E=4.10E-19\text{ }J \end{gathered}`

Those are the answers.