A small piece of mass m moves in such a way the P.E. =`-(1)/(2)mkr^(2)`. Where k is a constant and r is the distance of the particle from origin. Assuming Bohr's model of quantization of angular momentum and circular orbit, r is directly proportional to :
A small piece of mass m moves in such a way the P.E. =`-(1)/(2)mkr^(2)`. Where k is a constant and r is the distance of the particle from origin. Assuming Bohr's model of quantization of angular momentum and circular orbit, r is directly proportional to :
A
`n^(2)`
B
n
C
`sqrt(n)`
D
none of these
Text Solution
Verified by Experts
|
Topper's Solved these Questions
Similar Questions
Explore conceptually related problems
For a hypothetical hydrogen like atom, the potential energy of the system is given by U(r)=(-Ke^(2))/(r^(3)) , where r is the distance between the two particles. If Bohr's model of quantization of angular momentum is applicable then velocity of particle is given by:
A paricle of charge q and mass m moves in a circular orbit of radius r with angular speed omega . The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on.
Knowledge Check
A solid sphere of radius R has a charge Q distributed in its volume with charge density rho = k r ^(2) where kanda are constants and r is the distance from its center. If the electric field at r=R/2 is 1/16 times that at r=R, find value of a.
A solid sphere of radius R has a charge Q distributed in its volume with charge density rho = k r ^(2) where kanda are constants and r is the distance from its center. If the electric field at r=R/2 is 1/16 times that at r=R, find value of a.
A
2
B
1
C
3
D
4
Similar Questions
Explore conceptually related problems
A particle of mass m is moving in yz-plane with a uniform velocit v with its trajectory running paralel to + ve y-axis and intersecting z-axis at z = a show in the figure. The change in its angular momentum about the origin as it bounces elastically from a wal at y = constant is
The plane denoted by P_1 : 4x+7y+4z+81=0 is rotated through a right angle about its line of intersection with plane P_2 : 5x+3y+10z=25 . If the plane in its new position be denoted by P, and the distance of this plane from the origin is d, then the value of [(k)/(2)] (where[.] represents greatest integer less than or equal to k) is....
A circle is the locus of a point in a plane such that its distance from a fixed point in the plane is constant. Anologously, a sphere is the locus of a point in space such that its distance from a fixed point in space in constant. The fixed point is called the centre and the constant distance is called the radius of the circle/sphere. In anology with the equation of the circle |z-c|=a , the equation of a sphere of radius a is |r-c|=a , where c is the position vector of the centre and r is the position vector of any point on the surface of the sphere. In Cartesian system, the equation of the sphere, with centre at (-g, -f, -h) is x^2+y^2+z^2+2gx+2fy+2hz+c=0 and its radius is sqrt(f^2+g^2+h^2-c) . Q. Equation of the sphere having centre at (3, 6, -4) and touching the plane rcdot(2hat(i)-2hat(j)-hat(k))=10 is (x-3)^2+(y-6)^2+(z+4)^2=k^2 , where k is equal to
A star like the sun has several bodies moving around it at different distances. Consider that all of them are moving in circular orbits. Let r be the distance of the body frm the centre of the star and let its linear velocity be v, angular velocity omega , kinetic energy K, gravitational potential energy U, total energy E and angular momentum p. As the radius r of the orbit increases, determine which of the above quantities increase and which one decrease.
An artificial satellite is revolving around a planet fo mass M and radius R, in a circular orbit of radius r. From Kepler's third law about te period fo a satellite around a common central bdy, square of the period of revolution T is proportional to the cube of the radius of the orbit r. Show usingn dimensional analysis, that T = k/R sqrt((r^3)/(g)) , where k is a dimensionless constant and g is acceleration due to gravity.
Solar Constant (s) : s =((r )/(R ))^(2)sigmaT^(4) , where r= radius of sun ,R= distance of the earth from the centre of sum , T= absolute temperature of sun . Value of solar constant is 1.937 "cal cm"^(-2) "min"^(-1) . Is the statement true?
A particle P starts from the point z_0=1+2i , where i=sqrt(-1) . It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point z_1dot From z_1 the particle moves sqrt(2) units in the direction of the vector hat i+ hat j and then it moves through an angle pi/2 in anticlockwise direction on a circle with centre at origin, to reach a point z_2dot The point z_2 is given by