Advertisements
Advertisements
Question
Using Bohr’s Theory of hydrogen atom, obtain an expression for the velocity of an electron in the nth orbit of an atom.
Advertisements
Solution
Let ‘e’, ‘m’, and ‘v’ be the charge, mass, and velocity of electrons, respectively, and ‘r’ is the radius of the orbit.
The positive charge on the nucleus is Ze, where Z is the atomic number (in case of hydrogen atom Z = 1).
As the electrostatic force of attraction provides the centripetal force.
`(mv^2)/r = 1/(4piepsilon_0) (("Ze") xx "e")/r^2`
`=> mv^2 = "Ze"^2/(4piepsilon_0r)`
`=> v = sqrt("Ze"^2/(4piepsilon_0" rm"))`
APPEARS IN
RELATED QUESTIONS
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?
Use Bohr’s model of hydrogen atom to obtain the relationship between the angular momentum and the magnetic moment of the revolving electron.
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)
If the radius of first electron orbit in hydrogen atom be r then the radius of the fourth orbit ill be ______.
Using Bohr's postulates derive the expression for the radius of nth orbit of the electron.
The simple Bohr model cannot be directly applied to calculate the energy levels of an atom with many electrons. This is because ______.
If a proton had a radius R and the charge was uniformly distributed, calculate using Bohr theory, the ground state energy of a H-atom when (i) R = 0.1 Å, and (ii) R = 10 Å.
The first ionization energy of H is 21.79 × 10-19 J. The second ionization energy of He atom is ______ × 10-19J.
A 20% efficient bulb emits light of wavelength 4000 Å. If the power of the bulb is 1 W, the number of photons emitted per second is ______.
[Take, h = 6.6 × 10-34 J-s]
