A particle of mass m moves in a circular orbit in a central potential field U ( r )= U 0 r 4. If Bohr's quantization conditions are applied, radii of possible orbitals r n vary with n 1 / α, where α is .

Question

A particle of mass m moves in a circular orbit in a central potential field U ( r )= U 0 r 4. If Bohr's quantization conditions are applied, radii of possible orbitals r n vary with n 1 / α, where α is . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

F =(- dU / dr )=-4 U 0 r 3=( mv 2/ r ) mv 2=4 U 0 r 4 v propto r 2 mvr =( nh /2 π) r 3 propto n r propto n 1 / 3 =3

Q. A particle of mass $m$ moves in a circular orbit in a central potential field $U (r) = U_{0} r^{4}$ . If Bohr's quantization conditions are applied, radii of possible orbitals $r_{n}$ vary with $n^{1/ α}$ , where $α$ is ________.

$F = \frac{- d U}{d r} = - 4 U_{0} r^{3} = \frac{m v ^{2}}{r}$
$m v^{2} = 4 U_{0} r^{4}$
$v \propto r^{2}$
$m v r = \frac{nh}{2 π}$
$r^{3} \propto n$
$r \propto n 1/3$
$= 3$

Q. A particle of mass m moves in a circular orbit in a central potential field U(r)=U0​r4. If Bohr's quantization conditions are applied, radii of possible orbitals rn​ vary with n1/α, where α is ________.

F=dr−dU​=−4U0​r3=rmv2​ mv2=4U0​r4 v∝r2 mvr=2πnh​ r3∝n r∝n1/3 =3

Q. A particle of mass $m$ moves in a circular orbit in a central potential field $U (r) = U_{0} r^{4}$ . If Bohr's quantization conditions are applied, radii of possible orbitals $r_{n}$ vary with $n^{1/ α}$ , where $α$ is ________.

$F = \frac{- d U}{d r} = - 4 U_{0} r^{3} = \frac{m v ^{2}}{r}$
$m v^{2} = 4 U_{0} r^{4}$
$v \propto r^{2}$
$m v r = \frac{nh}{2 π}$
$r^{3} \propto n$
$r \propto n 1/3$
$= 3$