Advertisements
Advertisements
प्रश्न
Using Bohr's postulates of the atomic model, derive the expression for radius of nth electron orbit. Hence obtain the expression for Bohr's radius.
Advertisements
उत्तर
According to the postulates of Bohr’s atomic model, the electrons revolve around the nucleus only in those orbits for which the angular momentum is the integral multiple of `h/(2pi)`
`:.L=(nh)/(2pi)`
Angular momentum is given by
L = mvr
According to Bohr’s 2nd postulate
`L_n=mv_nr_n=(nh)/(2pi)`
n → Principle quantum
vn → Speed of moving electron in the nth orbit
rn→ Radius of nthorbit
`v_n=e/(sqrt(4piin_0mr_n))`
`:.v_n=1/n e^2/(4piin_0) 1/((h/(2pi)))`
`:.r_n=(n^2/m)(h/(2pi))^2 (4piin_0)/e^2`
For n = 1 (innermost orbit),
`r_1=(h^2in_0)/(pime^2)`
This is the expression for Bohr's radius.
APPEARS IN
संबंधित प्रश्न
What is the maximum number of emission lines when the excited electron of an H atom in n = 6 drops to the ground state?
Calculate the radius of Bohr’s fifth orbit for hydrogen atom
The Bohr radius is given by `a_0 = (∈_0h^2)/{pime^2}`. Verify that the RHS has dimensions of length.
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?
According to Bohr's theory, an electron can move only in those orbits for which its angular momentum is integral multiple of ____________.
What is the energy in joules released when an electron moves from n = 2 to n = 1 level in a hydrogen atom?
The spectral line obtained when an electron jumps from n = 5 to n = 2 level in hydrogen atom belongs to the ____________ series.
The radius of the third Bohr orbit for hydrogen atom is ____________.
According to Bohr's model of hydrogen atom, an electron can revolve round a proton indefinitely, if its path is ______.
The inverse square law in electrostatics is |F| = `e^2/((4πε_0).r^2)` for the force between an electron and a proton. The `(1/r)` dependence of |F| can be understood in quantum theory as being due to the fact that the ‘particle’ of light (photon) is massless. If photons had a mass mp, force would be modified to |F| = `e^2/((4πε_0)r^2) [1/r^2 + λ/r]`, exp (– λr) where λ = mpc/h and h = `h/(2π)`. Estimate the change in the ground state energy of a H-atom if mp were 10-6 times the mass of an electron.
