Advertisements
Advertisements
प्रश्न
The Bohr radius is given by `a_0 = (∈_0h^2)/{pime^2}`. Verify that the RHS has dimensions of length.
Advertisements
उत्तर
The dimensions of ε0 can be derived from the formula given below:
`a = (epsilon_0h^2)/(pime^2) = (A^2T^0(ML^2 T^-1)^2)/(L^2ML^-2 (AT)^2)`
`=(M^2L^2T^-2)/(M^2L^3T^-2) = L`
Clearly, a0 has the dimensions of length.
APPEARS IN
संबंधित प्रश्न
State Bohr’s third postulate for hydrogen (H2) atom. Derive Bohr’s formula for the wave number. Obtain expressions for longest and shortest wavelength of spectral lines in ultraviolet region for hydrogen atom
The energy associated with the first orbit in the hydrogen atom is - 2.18 × 10-18 J atom-1. What is the energy associated with the fifth orbit?
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.
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.
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.
Using Bohr’s postulates, derive the expression for the frequency of radiation emitted when electron in hydrogen atom undergoes transition from higher energy state (quantum number ni) to the lower state, (nf).
When electron in hydrogen atom jumps from energy state ni = 4 to nf = 3, 2, 1, identify the spectral series to which the emission lines belong.
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?
A positive ion having just one electron ejects it if a photon of wavelength 228 Å or less is absorbed by it. Identify the ion.
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.
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.
In which of the following systems will the wavelength corresponding to n = 2 to n = 1 be minimum?
The radius of the third Bohr orbit for hydrogen atom is ____________.
According to Bohr’s theory, the angular momentum of an electron in 5th orbit is ______.
In Bohr model of hydrogen atom, which of the following is quantised?
Using Bohr's postulates derive the expression for the radius of nth orbit of the electron.
Using Bohr model, calculate the electric current created by the electron when the H-atom is in the ground state.
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 ______.
How much is the angular momentum of an electron when it is orbiting in the second Bohr orbit of hydrogen atom?
The radius of hydrogen atom in the ground state is 0.53 Å. The radius of Li2+ ion (atomic number = 3) in a similar state is ______.
