###### Advertisements

###### Advertisements

What is the shortest wavelength present in the Paschen series of spectral lines?

###### Advertisements

#### Solution

Rydberg’s formula is given as:

` "hc"/lambda = 21.76 xx 10^(-19) [1/"n"_1^2 - 1/"n"_2^2]`

Where,

h = Planck’s constant = 6.6 × 10^{−34} Js

c = Speed of light = 3 × 10^{8 }m/s

(n_{1} and n_{2} are integers)

The shortest wavelength present in the Paschen series of the spectral lines is given for values n_{1 }= 3 and n_{2} = ∞.

`"hc"/lambda = 21.76 xx 10^(-19) [1/(3)^2 - 1/(∞)^2]`

`lambda = (6.6 xx 10^(-34) xx 3 xx 10^8 xx 9)/(21.76 xx 10^(-19)`

= 8.189 × 10^{−7 }m

= 818.9 nm

#### APPEARS IN

#### RELATED QUESTIONS

An electron jumps from fourth to first orbit in an atom. How many maximum number of spectral lines can be emitted by the atom? To which series these lines correspond?

In both β^{−} and β^{+} decay processes, the mass number of a nucleus remains the same, whereas the atomic number Z increases by one in β^{−} decay and decreases by one in β^{+} decay. Explain giving reason.

Determine the series limit of Balmer, Paschen, and Pfund series, given the limit for Lyman series is 912 Å.

If wavelength for a wave is `lambda = 6000 Å,` then wave number will be ____________.

Which of the following transition will have highest emission frequency?

The energy (in eV) required to excite an electron from n = 2 to n = 4 state in hydrogen atom is ____________.

Let v_{1} and v_{3} be the frequency for series limit of Balmer and Paschen series respectively. If the frequency of first line of Balmer series is v_{2} then, relation between v_{1} and v_{2} and v_{3} is ____________.

The radii of the first four Bohr orbits of hydrogen atom are related as ____________.

If the mass of the electron is reduced to half, the Rydberg constant ______.

In hydrogen spectrum, the wavelengths of light emitted in a series of spectral lines is given by the equation, `1/lambda` = R `(1/4^2 - 1/"n"^2)`, where n = 5, 6, 7...... and 'R' is Rydberg's constant. Identify the series and wavelength region.

Each element is associated with a ______.

Continuous spectrum is produced by ______.

An electron makes a transition from orbit n = 4 to the orbit n = 2 of a hydrogen atom. What is the wave number of the emitted radiations? (R = Rydberg's constant)

Absorption line spectrum is obtained ______.

To produce an emission spectrum of hydrogen it needs to be ______.

Show that the first few frequencies of light that is emitted when electrons fall to the n^{th} level from levels higher than n, are approximate harmonics (i.e. in the ratio 1 : 2 : 3...) when n >> 1.

What is the minimum energy that must be given to a H atom in ground state so that it can emit an H_{γ} line in Balmer series. If the angular momentum of the system is conserved, what would be the angular momentum of such H_{γ} photon?

The first four spectral lines in the Lyman series of a H-atom are λ = 1218 Å, 1028Å, 974.3 Å and 951.4 Å. If instead of Hydrogen, we consider Deuterium, calculate the shift in the wavelength of these lines.

Determine the shortest wavelengths of Balmer and Pasch en series. Given the limit for the Lyman series is 912 Å.

Determine the series limit of Balmer, Paschen and Brackett series, given the limit for Lyman series is 911.6 Å.

The first three spectral lines of H-atom in the Balmer series are given λ_{1}, λ_{2}, λ_{3} considering the Bohr atomic model, the wavelengths of the first and third spectral lines `(lambda_1/lambda_3)` are related by a factor of approximately 'x' × 10^{–1}. The value of x, to the nearest integer, is ______.

The frequencies for series limit of Balmer and Paschen series respectively are 'v_{1}' and 'v_{3}'. If frequency of first line of Balmer series is 'v_{2}' then the relation between 'v_{1}', 'v_{2}' and 'v_{3}' is ______.

In the hydrogen atoms, the transition from the state n = 6 to n = 1 results in ultraviolet radiation. Infrared radiation will be obtained in the transition.

The frequency of the series limit of the Balmer series of the hydrogen atoms of Rydberg’s constant R and velocity of light c is ______.

Find the wavelength and wave number of the first member of the Balmer series in Hydrogen spectrum. (`R =1.097xx10^7m^(-1)`)

The de-Broglie wavelength of the electron in the hydrogen atom is proportional to ______.

Calculate the wavelength of the first two lines in the Balmer series of hydrogen atoms.