Advertisements
Advertisements
Question
A beam of light having wavelengths distributed uniformly between 450 nm to 550 nm passes through a sample of hydrogen gas. Which wavelength will have the least intensity in the transmitted beam?
Advertisements
Solution
Given:
Minimum wavelength of the light component present in the beam, λ1 = 450 nm Energy associated (E1) with wavelength (λ1 ) is given by
E1 = `(hc)/(lamda_1)`
Here,
c = Speed of light
h = Planck's constant
`therefore E_1 = (1242)/(450)`
= 2.76 eV
Maximum wavelength of the light component present in the beam, = 550 nm
Energy associated (E2) with wavelength is given by
`E_2 = (hc)/( lamda)`
∴ `E_2 = 1242/550 = 2.228 = 2.26 eV`
The given range of wavelengths lies in the visible range.
`therefore n_1 = 2, n_2 = 3,4,5....`
Let E'2 , E'3 , E'4 and E'5 be the energies of the 2nd, 3rd, 4th and 5th states, res pectively.
`E_2 - E_3 = 13.6(1/4 - 1/9)`
=`(12. 6 xx 5)/30=1.9 eV`
`E_2- E_4 = 13.6 (1/4 - 1/16)`
= 2.55 eV
`E_2-E_2 = 13.6 (1/4 - 1/25)`
= `(10.5xx21)/100 = 2.856 eV`
Only, E'2 − E'4 comes in the range of the energy provided. So the wavelength of light having 2.55 eV will be absorbed.
`lamda = (1242)/2.55 = 487.5 nm`
= 487 nm
The wavelength 487 nm will be absorbed by hydrogen gas. So, wavelength 487 nm will have less intensity in the transmitted beam.
APPEARS IN
RELATED QUESTIONS
(i) State Bohr's quantization condition for defining stationary orbits. How does the de Broglie hypothesis explain the stationary orbits?
(ii) Find the relation between three wavelengths λ1, λ2 and λ3 from the energy-level diagram shown below.
Find the frequency of revolution of an electron in Bohr’s 2nd orbit; if the radius and speed of electron in that orbit is 2.14 × 10-10 m and 1.09 × 106 m/s respectively. [π= 3.142]
Explain, giving reasons, which of the following sets of quantum numbers are not possible.
- n = 0, l = 0, ml = 0, ms = + ½
- n = 1, l = 0, ml = 0, ms = – ½
- n = 1, l = 1, ml = 0, ms = + ½
- n = 2, l = 1, ml = 0, ms = – ½
- n = 3, l = 3, ml = –3, ms = + ½
- n = 3, l = 1, ml = 0, ms = + ½
Calculate the energy required for the process
\[\ce{He^+_{(g)} -> He^{2+}_{(g)} + e^-}\]
The ionization energy for the H atom in the ground state is 2.18 ×10–18 J atom–1
State Bohr's postulate to define stable orbits in the hydrogen atom. How does de Broglie's hypothesis explain the stability of these orbits?
The numerical value of ionization energy in eV equals the ionization potential in volts. Does the equality hold if these quantities are measured in some other units?
Find the wavelength of the radiation emitted by hydrogen in the transitions (a) n = 3 to n= 2, (b) n = 5 to n = 4 and (c) n = 10 to n = 9.
According to Maxwell's theory of electrodynamics, an electron going in a circle should emit radiation of frequency equal to its frequency of revolution. What should be the wavelength of the radiation emitted by a hydrogen atom in ground state if this rule is followed?
The dissociation constant of a weak base (BOH) is 1.8 × 10−5. Its degree of dissociation in 0.001 M solution is ____________.
According to Bohr's theory, an electron can move only in those orbits for which its angular momentum is integral multiple of ____________.
Ratio of longest to shortest wavelength in Balmer series is ______.
When an electric discharge is passed through hydrogen gas, the hydrogen molecules dissociate to produce excited hydrogen atoms. These excited atoms emit electromagnetic radiation of discrete frequencies which can be given by the general formula
`bar(v) = 109677 1/n_1^2 - 1/n_f^2`
What points of Bohr’s model of an atom can be used to arrive at this formula? Based on these points derive the above formula giving description of each step and each term.
Consider two different hydrogen atoms. The electron in each atom is in an excited state. Is it possible for the electrons to have different energies but same orbital angular momentum according to the Bohr model? Justify your answer.
The mass of a H-atom is less than the sum of the masses of a proton and electron. Why is this?
State Bohr's postulate to explain stable orbits in a hydrogen atom. Prove that the speed with which the electron revolves in nth orbit is proportional to `(1/"n")`.
The wavelength in Å of the photon that is emitted when an electron in Bohr orbit with n = 2 returns to orbit with n = 1 in H atom is ______ Å. The ionisation potential of the ground state of the H-atom is 2.17 × 10−11 erg.
In hydrogen atom, transition from the state n = 6 to n = 1 results in ultraviolet radiation. Infrared radiation will be obtained in the transition ______.
What is meant by ionisation energy?
Specify the transition of an electron in the wavelength of the line in the Bohr model of the hydrogen atom which gives rise to the spectral line of the highest wavelength ______.
State three postulates of Bohr's theory of hydrogen atom.
