Advertisements
Advertisements
प्रश्न
The Bohr radius is given by `a_0 = (∈_0h^2)/{pime^2}`. Verify that the RHS has dimensions of length.
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
What is the maximum number of emission lines when the excited electron of an H atom in n = 6 drops to the ground state?
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?
If the photon of the wavelength 150 pm strikes an atom and one of its inner bound electrons is ejected out with a velocity of 1.5 × 107 ms–1, calculate the energy with which it is bound to the nucleus.
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.
State Bohr's postulate to define stable orbits in the hydrogen atom. How does de Broglie's hypothesis explain the stability of these orbits?
The electron in hydrogen atom is initially in the third excited state. What is the maximum number of spectral lines which can be emitted when it finally moves to the ground state?
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?
A neutron having kinetic energy 12.5 eV collides with a hydrogen atom at rest. Nelgect the difference in mass between the neutron and the hydrogen atom and assume that the neutron does not leave its line of motion. Find the possible kinetic energies of the neutron after the event.
Suppose in an imaginary world the angular momentum is quantized to be even integral multiples of h/2π. What is the longest possible wavelength emitted by hydrogen atoms in visible range in such a world according to Bohr's model?
In which of the following systems will the wavelength corresponding to n = 2 to n = 1 be minimum?
Mention demerits of Bohr’s Atomic model.
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?
According to the Bohr theory of H-atom, the speed of the electron, its energy and the radius of its orbit varies with the principal quantum number n, respectively, as:
The ground state energy of hydrogen atoms is -13.6 eV. The photon emitted during the transition of electron from n = 3 to n = 1 unknown work function. The photoelectrons are emitted from the material with a maximum kinetic energy of 9 eV. Calculate the threshold wavelength of the material used.
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 ______.
Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen 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.
On the basis of Bohr's theory, derive an expression for the radius of the nth orbit of an electron of hydrogen atom.
