Question

A monochromatic radiation of wavelength 975 Å excites the hydrogen atom from its ground state to a higher state

Answer 1

Here, the question is incomplete . The complete question is that we have to find how many different spectral lines are possible in the resulting spectrum.Which transition corresponds to the longest wavelength ?

Here, it is given that wavelength = 975 Å

                                                      = 975 × 10⁻¹⁰ m

As, hydrogen atom is excited from its ground state .

Thus, n₁ = ground state = 1

According to formula -

1/λ = R(1/n₁² - 1/n₂²) , where R = Rydberg constant = 1.09 * 10⁷  m⁻¹

λ  = wavelength of radiation emitted

n₂  =  excited state

=> 1/975 × 10⁻¹⁰  = R(1/1 - 1/n₂²)

=>  1/975 × 10⁻¹⁰  = 1.09 * 10⁷(1/1 - 1/n₂²)

=>  0.941  =  (1/1 - 1/n₂²)

=>  n₂  = 4   (approx)

Thus, electron is excited from ground state to 4th energy level .

Now according to the formula -

Number of spectral lines = (n₂ - n₁ + 1)(n₂ - n₁)/2

                                          =  (4 - 1 + 1)(4 - 1)/2

                                          =  6

Thus, transition that corresponds to longest wavelength amongst them is

from n = 1  to n = 4 .