Advertisements
Advertisements
प्रश्न
What is the energy in joules, required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is –2.18 × 10–11 ergs.
Advertisements
उत्तर
Energy (E) of the nth Bohr orbit of an atom is given by,
`"E"_"n" = (-(2.18xx10^(-18))"Z"^2)/"n"^2`
Where,
Z = atomic number of the atom
Ground state energy = – 2.18 × 10–11 ergs
= - 2.18 × 10–11 × 10–7 J
= - 2.18 × 10–18 J
Energy required to shift the electron from n = 1 to n = 5 is given as:
ΔE = E5 – E1
`= (-(2.18xx10^(-18))(1)^2)/(5)^2 - (-2.18 xx 10^(-18))`
`= (2.18xx10^(-18))[1 - 1/25]`
`= (2.18xx10^(-18))(24/25)`
`= 2.0928 xx 10^(-18)"J"`
Wavelength of emitted light = `"hc"/"E"`
`= ((6.626xx10^(-34))(3xx10^(8)))/(2.0928xx10^(-18))`
`= 9.498 xx 10^(-8) "m"`
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?
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
How many electrons in an atom may have the following quantum numbers?
n = 4, `m_s = -1/2`
How many electrons in an atom may have the following quantum numbers?
n = 3, l = 0
- Using the Bohr’s model, calculate the speed of the electron in a hydrogen atom in the n = 1, 2 and 3 levels.
- Calculate the orbital period in each of these levels.
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.
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?
When a photon is emitted by a hydrogen atom, the photon carries a momentum with it. (a) Calculate the momentum carries by the photon when a hydrogen atom emits light of wavelength 656.3 nm. (b) With what speed does the atom recoil during this transition? Take the mass of the hydrogen atom = 1.67 × 10−27 kg. (c) Find the kinetic energy of recoil of the atom.
The light emitted in the transition n = 3 to n = 2 in hydrogen is called Hα light. Find the maximum work function a metal can have so that Hα light can emit photoelectrons from it.
Radiation from hydrogen discharge tube falls on a cesium plate. Find the maximum possible kinetic energy of the photoelectrons. Work function of cesium is 1.9 eV.
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.
Draw energy level diagram for a hydrogen atom, showing the first four energy levels corresponding to n=1, 2, 3 and 4. Show transitions responsible for:
(i) Absorption spectrum of Lyman series.
(ii) The emission spectrum of the Balmer series.
The energy of an electron in an excited hydrogen atom is - 3.4 eV. Calculate the angular momentum of the electron according to Bohr's theory. (h = 6.626 × 10-34 Js)
The binding energy of a H-atom, considering an electron moving around a fixed nuclei (proton), is B = `- (Me^4)/(8n^2ε_0^2h^2)`. (m = electron mass). If one decides to work in a frame of reference where the electron is at rest, the proton would be moving around it. By similar arguments, the binding energy would be
B = `- (Me^4)/(8n^2ε_0^2h^2)` (M = proton mass)
This last expression is not correct because ______.
The simple Bohr model cannot be directly applied to calculate the energy levels of an atom with many electrons. This is because ______.
An electron in H-atom makes a transition from n = 3 to n = 1. The recoil momentum of the H-atom will be ______.
The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, λ1/λ2, of the photons emitted in this process is ______.
According to Bohr's theory, the radius of the nth Bohr orbit of a hydrogen like atom of atomic number Z is proportional to ______.
For the reaction \[\ce{2NO2 (g) ⇌ N2O4(g)}\], when ΔS = −176.0 JK−1 and ΔH = −57.8 kj mol−1, the magnitude of ΔG at 298 K for the reaction is ______ kJ mol−1. (Nearest integer)
Which from following is CORREСТ relationship between wavelength and momentum of electron?
