Question

calculate the maximum wavelength in angstrom emitted in the balmer series of hydrogen spectra.Given Rydberg constant = 1.097^10^7m^-1​

Answer 1

Answer:

The answer will be 6565 Å.

Explanation:

So, basically what we have to do here is find the wavelength of red color light among all the spectral lines of Balmer series as it has maximum wavelength. So, let's find it.

(Why red light? Because Balmer had discovered the series of only visible light on spectrum due to emitted electromagnetic radiation from hydrogen gas (which he named Balmer series) and in visible light we know that red light has maximum wavelength.)

For Balmer series, Balmer had given a formula which describes the relation between wavenumber (which is the reciprocal of wavelength) and the spectral line of hydrogen spectrum that he had described as radial quantum number or principal quantum number of the electron and that formula is;

              1/λ = R (1/2² - 1/n²);                                      (i)

     here, λ = wavelength of the particular spectral line for which the value of n will be assigned.

              R = Rydberg Constant;

              n = particular value of spectral line of the hydrogen spectrum which will always be greater than 2.

Here, n will be assigned the value of red light (which is 3) as it has maximum wavelength in Balmer series and that's what we've been asked to find.

Thus,

        n = 3;

        R = 1.097 * 10^7m^-1​;

Using eq. (i);

           1/λ = R (1/2² - 1/n²);  

          1/λ = (1.097 * 10^7m^-1) (1/4 - 1/(3)²);

         1/λ = (1.097 * 10^7m^-1) (1/4 - 1/9);

               = (1.097 * 10^7m^-1) (0.138);

               = 0.1523 * 10^7m^-1;

         1/λ = 1.523 * 10^6 m^-1;

Thus wavelength equals;

              1/λ = 1.523 * 10^6 m^-1;

                λ = 1/(1.523 * 10^6 m^-1);

                 λ = 1/(1.523 * 10^6) m;

                    = 0.6565 * 10^-6m;

                     = 6.565 * 10^-7 m;

Now, 1 Angstrom = 10^-10 m;

Thus, wavelength in Å = 6.565 * 10^-7 * 1/10^-10 Å;

                                     = 6.565 * 10^3 Å;

                                     = 6565 Å;

That's all.