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प्रश्न
On the basis of Bohr's theory, derive an expression for the radius of the nth orbit of an electron of hydrogen atom.
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उत्तर
Let r be the orbit's radius and e, m, and v represent the electron's charge, mass, and velocity. Ze represents the nucleus's positive charge. For an atom of hydrogen, Z = 1. The electrostatic force of attraction provides centripetal force.
Therefore,
`(mv^2)/r = 1/(4piε_0) (Ze xx e)/ r^2`
`mv^2 = (Ze^2)/(4piε_0r)` ...(i)
By first postulate:
`mvr = (nh)/(2pi)` ...(ii)
Where n is the quantum number.
Squaring equation (ii) and dividing by equation (i), we get:
`(m^2v^2r^2)/(mv^2) = (n^2h^2)/((4pi^2)/((Ze^2)/(4piε_0r)))`
Then, `r = (n^2h^2ε_0)/(piZe^2m)`
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संबंधित प्रश्न
Calculate the radius of second Bohr orbit in hydrogen atom from the given data.
Mass of electron = 9.1 x 10-31kg
Charge on the electron = 1.6 x 10-19 C
Planck’s constant = 6.63 x 10-34 J-s.
Permittivity of free space = 8.85 x 10-12 C2/Nm2
Explain, giving reasons, which of the following sets of quantum numbers are not possible.
- n = 0, l = 0, ml = 0, ms = + ½
- n = 1, l = 0, ml = 0, ms = – ½
- n = 1, l = 1, ml = 0, ms = + ½
- n = 2, l = 1, ml = 0, ms = – ½
- n = 3, l = 3, ml = –3, ms = + ½
- n = 3, l = 1, ml = 0, ms = + ½
The ratio of kinetic energy of an electron in Bohr’s orbit to its total energy in the same orbit is
(A) – 1
(B) 2
(C) 1/2
(D) – 0.5
The Bohr radius is given by `a_0 = (∈_0h^2)/{pime^2}`. Verify that the RHS has dimensions of length.
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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.
Mention demerits of Bohr’s Atomic model.
A set of atoms in an excited state decays ______.
Find the ratio of energies of photons produced due to transition of an election of hydrogen atom from its (i) second permitted energy level to the first level. and (ii) the highest permitted energy level to the first permitted level.
What is the velocity of an electron in the 3rd orbit of hydrogen atom if its velocity in the 1st orbit is v0?
