Question

When a low-pressure gas of hydrogen atoms is placed in a tube and a large voltage is applied to the end of the tube, the atoms will emit electromagnetic radiation and visible light can be observed. If this light passes through a diffraction grating, the resulting spectrum appears as a pattern of four isolated, sharp parallel lines, called spectral lines. Each spectral line corresponds to one specific wavelength that is present in the light emitted by the source. Such a discrete spectrum is referred to as a line spectrum.
What is the wavelength of the line corresponding to n =4 in the Balmer series? Express your answer in nanometers to three significant figures. EVO AV Om ? X (n) = 4.86.10? By the early 19th century, it was found that discrete spectra were produced by every chemical element in its gaseous slale. Even though these spectra were found to share the common feature of appearing as a set of isolated lines, it was observed that each element produces its own unique pattern of lines. This indicated that the light emitted by each element contains a specific set of wavelengths that is characteristic of that element. Submit Previous Answers Request Answer X Incorrect; Try Again; 19 attempts remaining

Answer 1

Answer:a)   λ = 4.862 10⁻⁷ m,  b)  λ = 4.341 10⁻⁷ m

Explanation:

The spectrum of hydrogen can be described by the expression

         

in the case of the initial state n = 2 this series is the Balmer series

a) Find the wavelength for n = 4

       

let's calculate

          = 1,097 10⁷ ()

         \frac{1}{ \lambda} = 1.097 10⁷ 0.1875 = 0.2056 10⁷

          λ = 4.862 10⁻⁷ m

b) n = 5

           

    \frac{1}{ \lambda} = 1,097 10⁷ ()

    \frac{1}{ \lambda} = 1.097 10⁷ 0.21 = 0.23037 10⁷

     λ = 4.341 10⁻⁷ m