Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
What is the maximum number of emission lines when the excited electron of an H atom in n = 6 drops to the ground state?
Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit.
The gravitational attraction between electron and proton in a hydrogen atom is weaker than the Coulomb attraction by a factor of about 10−40. An alternative way of looking at this fact is to estimate the radius of the first Bohr orbit of a hydrogen atom if the electron and proton were bound by gravitational attraction. You will find the answer interesting.
The difference in the frequencies of series limit of Lyman series and Balmer series is equal to the frequency of the first line of the Lyman series. Explain.
When a photon stimulates the emission of another photon, the two photons have
(a) same energy
(b) same direction
(c) same phase
(d) same wavelength
A parallel beam of light of wavelength 100 nm passes through a sample of atomic hydrogen gas in ground state. (a) Assume that when a photon supplies some of its energy to a hydrogen atom, the rest of the energy appears as another photon. Neglecting the light emitted by the excited hydrogen atoms in the direction of the incident beam, what wavelengths may be observed in the transmitted beam? (b) A radiation detector is placed near the gas to detect radiation coming perpendicular to the incident beam. Find the wavelengths of radiation that may be detected by the detector.
A neutron moving with a speed υ strikes a hydrogen atom in ground state moving towards it with the same speed. Find the minimum speed of the neutron for which inelastic (completely or partially) collision may take place. The mass of neutron = mass of hydrogen = 1.67 × 10−27 kg.v
The earth revolves round the sun due to gravitational attraction. Suppose that the sun and the earth are point particles with their existing masses and that Bohr's quantization rule for angular momentum is valid in the case of gravitation. (a) Calculate the minimum radius the earth can have for its orbit. (b) What is the value of the principal quantum number n for the present radius? Mass of the earth = 6.0 × 10−24 kg. Mass of the sun = 2.0 × 1030 kg, earth-sun distance = 1.5 × 1011 m.
Obtain Bohr’s quantisation condition for angular momentum of electron orbiting in nth orbit in hydrogen atom on the basis of the wave picture of an electron using de Broglie hypothesis.
Mention demerits of Bohr’s Atomic model.
The dissociation constant of a weak base (BOH) is 1.8 × 10−5. Its degree of dissociation in 0.001 M solution is ____________.
Which of these statements correctly describe the atomic model according to classical electromagnetic theory?
Consider aiming a beam of free electrons towards free protons. When they scatter, an electron and a proton cannot combine to produce a H-atom ______.
- because of energy conservation.
- without simultaneously releasing energy in the from of radiation.
- because of momentum conservation.
- because of angular momentum conservation.
If a proton had a radius R and the charge was uniformly distributed, calculate using Bohr theory, the ground state energy of a H-atom when (i) R = 0.1 Å, and (ii) R = 10 Å.
The inverse square law in electrostatics is |F| = `e^2/((4πε_0).r^2)` for the force between an electron and a proton. The `(1/r)` dependence of |F| can be understood in quantum theory as being due to the fact that the ‘particle’ of light (photon) is massless. If photons had a mass mp, force would be modified to |F| = `e^2/((4πε_0)r^2) [1/r^2 + λ/r]`, exp (– λr) where λ = mpc/h and h = `h/(2π)`. Estimate the change in the ground state energy of a H-atom if mp were 10-6 times the mass of an electron.
The radius of the innermost electron orbit of a hydrogen atom is 5.3 × 10–11m. The radius of the n = 3 orbit is ______.
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")`.
A hydrogen atom in its first excited state absorbs a photon of energy x × 10-2 eV and exited to a higher energy state where the potential energy of electron is -1.08 eV. The value of x is ______.
Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength λ. If R is the Rydberg constant then the principal quantum number n of the excited state is ______.
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 ______.
