Advertisements
Advertisements
प्रश्न
Using Bohr model, calculate the electric current created by the electron when the H-atom is in the ground state.
Advertisements
उत्तर
The equivalent electric current due to rotation of charge is given by `i = Q/T = Q(1/T) = Q xx f`, where `f` is the frequency.
In a Hydrogen atom, an electron in the ground state revolves in a circular orbit whose radius is equal to the Bohr radius (a0). Let the velocity of the electron is v.
∴ Number of revolutions per unit time `f = (2πa_0)/v`
The electric current is given by i = Q of, if Q charge flows in time T. Here, Q = e.
The electric current is given by `i = e((2πa_0)/v) = (2πa_0)/v e`.
Important points:
| Some other quantities for a revolution of electron in nth orbit | |||
| Quantity | Formula | Dependency on n and Z |
|
| 1. | Angular speed | `ω_n = v_n/r_n = (pimZ^2e^4)/(2ε_0^2n^3h^3)` | `ω_n ∝ Z^2/n^3` |
| 2. | Frequency | `v_n = ω_n/(2pi) = (mZ^2e^4)/(4ε_0^2n^3h^3)` | `v_n ∝ Z^2/n^3` |
| 3. | Time period | `T_n = 1/v_n = (4ε_0^2n^3h^3)/(mZ^2e^4)` | `T_n ∝ n^3/Z^2` |
| 4. | Angular momentum | `L_n = mv_nr_n = n(h/(2pi))` | `L_n ∝ n` |
| 5. | Corresponding current | `i_n = ev_n = (mZ^2e^5)/(4ε_0^2n^3h^3)` | `i_n ∝ Z^2/n^3` |
| 6. | Magnetic moment | `M_n = i_nA = i_n (pir_n^2)` (where `mu_0 = (eh)/(4pim)` Bhor magneton) | `M_n ∝ n` |
| 7. | Magnetic field | `B = (mu_0i_n)/(2r_n) = (pim^2Z^3e^7 m_0)/(8ε_0^3n^5h^5)` | `B ∝ Z^3/n^5` |
APPEARS IN
संबंधित प्रश्न
The longest wavelength doublet absorption transition is observed at 589 and 589.6 nm. Calculate the frequency of each transition and energy difference between two excited states.
- 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.
Using Bohr’s postulates, obtain the expressions for (i) kinetic energy and (ii) potential energy of the electron in stationary state of hydrogen atom.
Draw the energy level diagram showing how the transitions between energy levels result in the appearance of Lymann Series.
A beam of monochromatic light of wavelength λ ejects photoelectrons from a cesium surface (Φ = 1.9 eV). These photoelectrons are made to collide with hydrogen atoms in ground state. Find the maximum value of λ for which (a) hydrogen atoms may be ionized, (b) hydrogen atoms may get excited from the ground state to the first excited state and (c) the excited hydrogen atoms may emit visible light.
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.
In which of the following systems will the wavelength corresponding to n = 2 to n = 1 be minimum?
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.
Use Bohr’s model of hydrogen atom to obtain the relationship between the angular momentum and the magnetic moment of the revolving electron.
Calculate the de-Broglie wavelength associated with the electron revolving in the first excited state of the hydrogen atom. The ground state energy of the hydrogen atom is −13.6 eV.
A particle has a mass of 0.002 kg and uncertainty in its velocity is 9.2 × 10−6 m/s, then uncertainty in position is ≥ ____________.
(h = 6.6 × 10−34 J s)
The energy associated with the first orbit of He+ is ____________ J.
If the radius of first electron orbit in hydrogen atom be r then the radius of the fourth orbit ill be ______.
Hydrogen atom has only one electron, so mutual repulsion between electrons is absent. However, in multielectron atoms mutual repulsion between the electrons is significant. How does this affect the energy of an electron in the orbitals of the same principal quantum number in multielectron atoms?
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.
For the ground state, the electron in the H-atom has an angular momentum = h, according to the simple Bohr model. Angular momentum is a vector and hence there will be infinitely many orbits with the vector pointing in all possible directions. In actuality, this is not true ______.
The mass of a H-atom is less than the sum of the masses of a proton and electron. Why is this?
Given below are two statements:
Statements I: According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increases with decrease in positive charges on the nucleus as there is no strong hold on the electron by the nucleus.
Statement II: According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increase with a decrease in principal quantum number.
In light of the above statements, choose the most appropriate answer from the options given below:
The energy required to remove the electron from a singly ionized Helium atom is 2.2 times the energy required to remove an electron from Helium atom. The total energy required to ionize the Helium atom completely is ______.
If 13.6 eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from n = 2 is ______.
Energy and radius of first Bohr orbit of He+ and Li2+ are:
[Given RH = −2.18 × 10−18 J, a0 = 52.9 pm]
