Home
Class 12
PHYSICS
The electirc potential between a proton ...

The electirc potential between a proton and an electron is given by `V = V_0 ln (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)`

A

`r_(n) prop n`

B

`r_(n) prop = (1)/(2)`

C

`r_(n) prop n^(2)`

D

`r_(n) prop (1)/(n^(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
Given that `v = v_(o) log_(e) (r//r_(o))`
field `E = (-dv)/(dr)` or `E = -V_(o) ((r_(o))/(r ))`
Now `eE = (mv^(2))/(r )` or `(eV_(o)r_(o))/(r ) = (mv_(o)^(2))/(r )`
`:. V = ((ev_(o)r_(o))/(m))^(1//2)`
Now `mv = (mev_(o)r_(o))1^(1//2) =` constant
`:. mvr = (nh)/(2 pi)` Bohr's quantum condition
or `r prop n`
Promotional Banner

Similar Questions

Explore conceptually related problems

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)?

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)?

Prove that sum_(r = 0)^n r^2 . C_r = n (n +1).2^(n-2)

If n is an even natural number , then sum_(r=0)^(n) (( -1)^(r))/(""^(n)C_(r)) equals

Find sum of sum_(r=1)^n r . C (2n,r) (a) n*2^(2n-1) (b) 2^(2n-1) (c) 2^(n-1)+1 (d) None of these

If ""^(n)C _r denotes the numbers of combinations of n things taken r at a time, then the expression ""^(n) C_(r+1) +""^(n)C_(r-1) +2 xx ""^(n)C_r equals

Which of the following expressions represents the spectrum of Balmer series (If n is the principal quantum number of higher energy level) in Hydrogen atom ? (a) overset-v=(R(n-1)(n+1))/n^(2) (b) overset-v=(R(n-2)(n+2))/(4n^(2)) (c) overset-v=(R(n-2)(n+2))/(n^(2)) (d) overset-v=(R(n-1)(n+1))/(4n^(2))

Prove that sum_(r=0)^n r(n-r)(^nC_ r)^2=n^2(^(2n-2)C_n)dot

Prove that sum_(r = 0)^n r^3 . C_r = n^2 (n +3).2^(n-3)

sum_(r=0)^n (-1)^r .^nC_r (1+rln10)/(1+ln10^n)^r