Advertisements
Advertisements
प्रश्न
Use Bohr's postulate to prove that the radius of nth orbit in a hydrogen atom is proportional to n2.
Advertisements
उत्तर
The necessary centripetal force for the rotation of an electron is supplied by the electrostatic force between the electron and the nucleus.
`"mv"^2/"r" = (1/(4πε_0))("e"^2/"r"^2)` ....[putting Z = 1]
Or, mv2 = `"e"^2/(4πε_0"r")` .....(i)
From Bohr's theory,
mvr = `"nh"/(2π)`
∴ v = `"nh"/(2π"mr")`
Putting in equation (i)
`"m"("nh"/(2π"mr"))^2 = "e"^2/(4πε_0"r")`
Or, r = `(ε_0"n"^2"h"^2)/(π"me"^2)`
In general,
rn = `(ε_0"n"^2"h"^2)/(π"me"^2)`
∴ `"rn" ∝ "n"^2`
APPEARS IN
संबंधित प्रश्न
If the velocity of the electron in Bohr’s first orbit is 2.19 × 106 ms-1, calculate the de Broglie wavelength associated with it.
Which of the following parameters are the same for all hydrogen-like atoms and ions in their ground states?
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.
In which of the following systems will the wavelength corresponding to n = 2 to n = 1 be minimum?
What is the energy in joules released when an electron moves from n = 2 to n = 1 level in a hydrogen atom?
In Bohr model of hydrogen atom, which of the following is quantised?
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)
Derive an expression for the frequency of radiation emitted when a hydrogen atom de-excites from level n to level (n – 1). Also show that for large values of n, this frequency equals to classical frequency of revolution of an electron.
The ratio of the ionization energy of H and Be+3 is ______.
How will the energy of a hydrogen atom change if n increases from 1 to ∞?
