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
State Bohr’s postulate of hydrogen atom which successfully explains the emission lines in the spectrum of hydrogen atom. Use Rydberg formula to determine the wavelength of Hα line. [Given: Rydberg constant R = 1.03 × 107 m−1]
If the velocity of the electron in Bohr’s first orbit is 2.19 × 106 ms-1, calculate the de Broglie wavelength associated with it.
In Bohr’s model of the hydrogen atom, the radius of the first orbit of an electron is r0 . Then, the radius of the third orbit is:
a) `r_0/9`
b) `r_0`
c) `3r_0`
d) `9r_0`
Using Bohr's postulates, derive the expression for the orbital period of the electron moving in the nth orbit of hydrogen atom ?
Which of the following parameters are the same for all hydrogen-like atoms and ions in their ground states?
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.
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
If l3 and l2 represent angular momenta of an orbiting electron in III and II Bohr orbits respectively, then l3: l2 is :
How are various lines of Lyman series formed? Explain on the basis of Bohr’s theory.
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.
Use Bohr's postulate to prove that the radius of nth orbit in a hydrogen atom is proportional to n2.
The value of angular momentum for He+ ion in the first Bohr orbit is ______.
An electron in H-atom makes a transition from n = 3 to n = 1. The recoil momentum of the H-atom will be ______.
The line at 434 nm in the Balmer series of the hydrogen spectrum corresponds to a transition of an electron from the nth to second Bohr orbit. The value of n is ______.
The wavelength of the second line of the Balmer series in the hydrogen spectrum is 4861 Å. Calculate the wavelength of the first line of the same series.
The de Broglie wavelength of an electron in the first Bohr’s orbit of hydrogen atom is equal to ______.
What spectrum would an atom emit if its electron spiralled inward while emitting radiation continuously?
