A particle of mass m moves in a circular orbit in a central potential field U r = 1 2 k r 2 . If Bohr's quantization conditions are applied, radii of possible orbitals and energy levels vary with quantum number n as:

Question

Aicharya · Accepted Answer

F r = - d U d r = - k r For circular motion | F r | = k r = m v 2 r &#8658; k r 2 = m v 2 ........(i) Bohr's quantization &#8658; m v r = n h 2 &#960; ....(ii) From (i) and (ii) m 2 v 2 m = k r 2 &#8658; 1 m n h 2 &#960; r 2 = k r 2 &#8658; n 2 h 2 4 &#960; 2 m k = r 4 &#8658; r = h 2 4 &#960; 2 m k 1 / 4 n 1 / 2 r &#8733; n From equation (i) U &#8733; n K E = 1 2 m v 2 ;&#160; P E = 1 2 k r 2 E = K + U = 1 2 m v 2 + 1 2 k r 2 = k r 2 &#8733; n

A particle of mass m moves in a circular orbit in a central potential field U r = 1 2 k r 2 . If Bohr's…

Solution

A particle of mass m moves in a circular orbit in a central potential field U r = 1 2 k r 2 . If Bohr&#39;s…

Solution

A particle of mass m moves in a circular orbit in a central potential field U r = 1 2 k r 2 . If Bohr's…