The elecrric potential between a proton and as electron is given by `V= V_(0) ln (r /r_(0))` , where`r_(0)` is a constant . Assuming Bohr's model to be applicable , write variation of `r_(n)` with `n`, `n` being the principal quantum number ?
A
`r_(n) prop n `
B
`r_(n) prop 1//n `
C
`r_(n) prop n^(2)`
D
`r_(n) prop 1//n^(2) `
Text Solution
Verified by Experts
The correct Answer is:
A
Given potential energy between electron and proton `= eV_(0) log ( r)/(r_(0)) [:. |U| = eV]` `:. |F| = (d)/(dr)[eV_(0) log_(e) (r )/(r_(0))] = ev_(0))/(r_(0)) xx (1)/(r )` But this force act as centripetal force `:. (m nu^(2))/(r ) = (ev_(0))/(rr_(0)) rArr m nu^(2) = (ev_(0))/(r_(0)0 `...(i) by Bohr's postulate, `m nu r = (nh)/(2pi)` ...(ii) From (i) and (ii) , ` (m^(2) nu ^(2) r^(2))/(m nu^(2)) = (n^(2) h ^(2) r_(0))/(4 pi V_(0) me) rArr r = prop n `
SUNIL BATRA (41 YEARS IITJEE PHYSICS)|Exercise Comprehension Based Questions|2 Videos
MOVING CHARGES AND MAGNETISM
SUNIL BATRA (41 YEARS IITJEE PHYSICS)|Exercise MCQs(d )|1 Videos
Similar Questions
Explore conceptually related problems
The electirc potential between a proton and an electron is given by V = V_0 in (r )/(r_0) , where r_0 is a constant. Assuming Bhor model to be applicable, write variation of r_n with n, being the principal quantum number. (a) r_n prop n (b) r_n prop (1)/(n) (c ) r_n^2 (d) r_n prop (1)/(n^2)
The potential of an atom is given by V=V_(0)log_(e)(r//r_(0)) where r_(0) is a constant and r is the radius of the orbit Assumming Bohr's model to be applicable, which variation of r_(n) with n is possible (n being proncipal quantum number)?
Supose the potential energy between electron and porton a distance r is given by U=-(Ke^(2))/(3r^(3)) Assuming Bohar's Model to be valid for this atom if the speed of elctron in n^(th) orbit depends on the prinicpal quantum number n as v oon^(x) then find the vlaue of x.
In a hypothetical atom, potential energy between electron and proton at distance r is given by ((-ke^(2))/(4r^(2))) where k is a constant Suppose Bohr theory of atomic structrures is valid and n is principle quantum number, then total energy E is proportional to
Suppose the potential energy between electron and proton at a distance r is given by U= Ke l n(r )/(a) , where r lt a and k, e,a are positive constants. Use Bohr's theory to obtain the energy of nth energy level of such an atom.
The potential energy of a particle moving in a circular path is given by U = U_0 r^4 where r is radius of circular path. Assume bohr model to be valid. The radius of nth orbit is r prop n^(1/alpha) where alpha is
Which of the following curves may represent the radius of orbit (r_(n)) in H-atoms as a function of principal quantum number (n)
The electron in a hydrogen atom makes a trapsition n_(1) to n_(2), where n_(1) and n_(2) are the principal quantum numbers of the two energy states. Assume Bohr's model to be velid. The time period of the electron in the initial state is eight time that in the final static. what are the possible value of n_(1) and n_(2) ?
Suppose the potential energy between an electron and a proton at a distance r is given by Ke^(2)// 3 r^(3) . Application of Bohr's theory tohydrogen atom in this case showns that
SUNIL BATRA (41 YEARS IITJEE PHYSICS)-MODERN PHYSICS-MCQ (One Correct Answer
